The Third Part Of The Last Discussion

These semi-groups that here arbitrarily commute kinematically phenomenal discharge of those related superstrings, of one or more of the said orbifolds relative to one another, causes the spin-symmetries that become covariant here via wave co-axials that covariantly differentiate thru a Lagrangian that occurs over an arbitary Fourier Transform so as to curve with relative hermicity on account of the related Njenhuis wave-tug permittivity eigenforces and the related Njenhuis wave-tug impedance eignforces.  The Laplacian mapping of the path that relates to what I just described is what I am trying to convey here.  This happens in such a manner so that the Campbell/Hausendorf/Campbell Hausendorf and Zero-Norm Projections that are formed on account of this, here, arbitrarily forms a hermitian motion via the Greene Function known of as the Fujikawa Coupling.  In other related cases, such an activity may form other types of Yakawa Couplings.     
I will continue with the suspence later!  Sincerely, Samuel David Roach.

A Continuation Of Yesterday

This is so that the previously mentioned homogeneous wave permittivity will allow for the commutation of spin symmetry via the indices that are local to all three substringualr groups at one group metric or another on their way thru the Continuum -- differentiating time-wise with the chirality of the residue as it vibrates thru, while being in proportion to the related norm-conditions that are in transition by being in  covariance with the angular momentum of each sector of the mentioned substringular residue.  In the meanwhile, the tri-local substringular encodements converge the locus of the related orbifolds in proportion to the euclidean-based even distribution of their wave propagation and residue.       
I will do the third part of this discussion tommorrow!  I will talk to you then.  Sincerely, Sam Roach.

Some Knowledge About Covariant Groups

Let's say that three covariant substringular groups going through a Fourier Transformation were Njenhuisly perturbated, to where the three groups which here represent three orbifolds consequently produce a perturbation in the related covariant codifferentiation that will potentially alter any potential Kaluza-Klein topology in the said three orbifolds into a Yang-Mills topology.  But, here, the homotopic residue of each mentioned substringular group will maintain its Fourier-Based generation of substringular field as the said groups propagate along the Ultimon.  I will continue when I have the time!  Sam.    

Some More About The Light-Cone-Gauge

As to the discussion about two sets of superstrings that differentiate covariantly over a given arbitrary Fourier Transformation:  The discribed activity here repeats its mentioned mode in a manner so that it involves a reiterated sequential series of corresponding instantons that strays in a general spot in such a manner so as to not go as a group through a discrete unitary and/or tree-amplitude-based unitized directoral.  The more that a Wilson-Line develops in terms of having more of a basis of unitization among the superstrings that form the said two mentioned substringular groups taken individually -- and especially when such unitization combines the two said groups -- that potentially causes these to form a syncronization that will pull these into a motion that involves a discrete Lagrangian.  Then, such a unitization may spontaneously allign the parity between these related superstrings in such a manner that these would thence converge the arbitrarily related holonomic discharge of substringular field (mini-strings of which form the physical entity of the said field) which, if the Noether-Based flow of  the prior mentioned substringular group catches up with what was earlier the prior mentioned arbitrary tachyonic-based substringular group, this would then need to be on account of what would appertain to a minor spuriousness in the tachyonic scattering of both substringular groups. An example of this, when photons scatter, these are initially tachyonic for relatively few instantons.  Right after that, the said photons that just scattered slow down more than these initially sped up, as according to Snell's Law.  These photons -- in the process -- catch up to the orbifolds in which these are to quantize with in such a manner that photons that travel outside of a vacuum always travel slower On Average than these would travel in a vacuum.  Again, this happens as Snell's Law indicates.  This will be much further discussed in future books that I wrote. 
I will continue with the suspence later!  Sincerley, Samuel Roach.            

About The Difference Between The Two General Types Of LCG

With a light-cone-gauge eigenstate that corresponds to a one-dimensional superstring of energy permittivity, the conical shape that may be mapped out during the activity of BRST is a planar or Minkowski partial field that bears two isomorphic hyperbolic ends that form a kinematic flowing of a surface area that is redistributed as the activity that happens during BRST is progressing.  Yet, with a light-cone-gauge eigenstate that corresponds to a two-dimensional superstring of energy permittivity, the conical shape that may be mapped out during the activity of BRST is a volume-based or Hilbert partial field that bears a region of concentric hyperbolic ends that are relatively homeomorphic per frame -- although the kinematic flow forms a permutating shape that acts as a region that is locally Ward three-dimensional .  So, as the field of a light-cone-gauge is the most important field appertaining to both the interaction of corresponding superstrings with other superstrings of energy permittivity and also to the initializing of the determination as to the succeeding delineation of the related superstrings, the constant variation of the respective Minkowski and Hilbert conical regions that flow in the general locus of the region that exists in-between a superstring and its corresponding Fadeev-Popov-Trace works to form a substrate for its interaction with its corresponding gauge-bosons so that the vibrations of the related light-cone-gauge eigenstates may harmonically in some cases -- or anharmonically in other cases -- cause the needed vibrations in Rarita Structure eigenstates so that both the Ricci Scalar will bear the necessary amplitude Hodge indices and also so that the appropriate norm projections may be able to interact with the correlative orbifolds and orbifold eigenstates in such a manner so that the Wick Action eigenstates may be able to indirectly cause that motion of Higgs Action eigenstates which causes the motion of Klein Bottle eigenstates to happen in such a manner so that Gaussian Transformaions may occur.  The pattern of the cohomological flow of the fields of light-cone-gauge eigenstates works to signal where the spatial transference of superstrings is to be redistributed -- the motion of the prior mentioned fields are the initial basis that helps to determine where the related superstrings of energy permittivity are to go next.  The manner of the mapping of the said conical relationships that I mentioned during BRST is based on the condition that exists once the related Polyakov Action eigenstates are well underway.  So, as the cites of the fields of superstrings are progressing during the period in which the Imaginary of Exchange of Real Residue is kinematic upon the related superstrings, the volume of the field partial that may be described as the field of first-ordered-light-cone-gauge eigenstates increases until the Polyakov Action appertaining to one multiplicitly covariant instanton is completed.  The effect of Lorentz-Four-Contractions is based on the condition that exists at metrical locus of the last frame of BRST.  So, when considering the proximity of superstrings with their corresponding Fadeev-Popov-Traces, the amplitude of the apexing of the Laplacian-based mapping as to the amount of light-cone-gauge field that exists per region at the end of BRST is Dirac in the relatively forward holomorphic direction and Reverse-Dirac in the relatively reverse holomorphic direction.  I will continue with the suspence later!  Sincerely, Sam Roach.  

Why The Light-Cone-Gauge Is Named What It Is

During the Polyakov Action, superstrings of discrete energy permittivity unstretch in terms of their length (for one-dimensional superstrings) or in terms of their circumference (in terms of two-dimensional supserstrings) to the inverse extent that the said mentioned superstrings are not totally contracted.  Throughout the duration of BRST -- which is when both the Bette Action and the Polyakov Action happen -- mini-string wave import is fed into the general locus of field partial in which the related first-ordered-light-cone-gauge eigenstate is existent at during the said duration of BRST.  The wave import that here describes the corresponding light-cone-gauge eigenstate, during the activity in which the Polyakov Action is happening, thus forms a cone-shaped field that may be mapped when one integrates the general region in which the mentioned given arbitrary light-cone-gauge eigenstate is working to provide a basis for a substrate in which gauge bosons may pluck these like a harp so as to form the necessary vibrations -- Schwinger Indices -- that are needed to covariantly inter-relate norm projections with externalized superstrings so that discrete energy may kinematically interact with other discrete energy.  The Polyakov Action happens to the inverse extent of Lorentz-Four-Contractions, and, Lorentz-Four-Contractions happen based on the relationship of superstrings to the motion and existence of light (quantized photons).  The integrated mapped sub-metric generalized partial field that exists as both a basis of substringular interaction and a basis for the springing of superstrings into that Ultimo;n Flow that gauges where a superstring is to be relocated during its next iteration forms a sloped conical concavity that apexes at the conipoints where the related mini-string segments are interwovenly tied in a kinematic manner at the related Fadeev-Popov-Trace that is most directly associated with the corresponding superstrings that are here undergoing Polyakov Action.  The corresponding mini-string segments are constantly fed wave import where the related light-cone-gauge eigenstate is kinematically differential during an eigenmetric of Polyakov Action.  The slope of a light-cone-gauge eigenstate during the Polyakov Action is hermitian when a corresponding superstring is orientable.  The light-cone-gauge is a gauge in the manner that it works to provide an initial basis for the determination of the redelineation of superstrings that most directly correspond with the related first-ordered-light-cone-gauge eigenstates.  There is a lot more that I wish to describe in relation to this.  I will continue with the suspense later!  Sincerely, Sam Roach.    

About Non Abelian Light-Cone-Gauge Nature

With a superstring that involves a Yang-Mills topology, the mini-string segments that most directly bind an arbitrary given superstring with its corresponding Fadeev-Popov-Trace bear a Laplacian-based sinusoidal differential delineation at the beginning of BRST.  A superstring that bears a Yang-Mills topology is said to have a non-abelian light-cone-gauge topology.  The manner in which the mentioned sinusoidal Laplacian-based delineation of the said mini-string segments that form a certain partial field between a given superstring and its corresponding Fadeev-Popov-Trace at the beginning frame of BRST will be further discussed during courses ten and twelve.  As BRST progresses during the ebbing action that I describe as the Imaginary Exchange of Real Residue (which happens throughout BRST -- and BRST involves virtually the whole duration of instanton), the differential arrangement of the initial said sinusoidal wave-pattern that corresponds with a here discussed non-abelian light-cone-gauge topology is altered in terms of its amplitude and its relatively standing frequency.  So, during the initial motion of the action of BRST in which the Imaginary Exchange of Real Residue begins to happen, the fractal modulus of the said sinusoidal delineation, that may be described as the most direct field partial that interconnects a given arbitrary superstring with its corresponding Fadeev-Popov-Trace, increases in its ability to keep unfrayed, while, simultaneously, the amplitude of the said relatively standing sinusoidal wave-patten delineation that forms the basis of the said given light-cone-gauge eigenstate decreases in terms of its scalar translation -- along with a decrease in the frequency of the vibration of the said first-ordered-light-cone-gauge eigenstate as the said eigenstate is beginning -- here -- to be plucked "like a harp" by the corresponding gauge-bosons that exist in the general local region where the mentioned light-cone-gauge eigenstate is differentiating during the BRST portion of a given arbitrary instanton.  I still have a lot more to say about this.  I will continue with the suspense later!  Sincerely, Samuel David Roach.

As To The Abelian Nature Of The Light-Cone-Gauge

The physical topological condition of the type of wave-tug that is mapped in a Laplacian manner so as to determine the general type of differential geometry of an arbitrary given first-ordered-light-cone-gauge, that is in the state that the said arbitrary first-ordered-light-cone-gauge is in, during the sub-metric that exists here, is during the initial frame of BRST.  So, if the light-cone-gauge topology that directly corresponds to a superstring bears a Kaluza-Klein topology, then, during the initial frame of sub-metric that is used to physically denote the Laplacian conditon of the start of BRST, for the here given individual superstring that is mentioned in this basic scenario, bears segments of mini-string that binds the corresponding superstring with its corelative Fadeev-Popov-Trace so as to form a field-pattern that is initially reltaively taught and non-sinusoidal -- with just enough of a leeway of "slack" so that the initial motion of the Imaginary Exchange of Real Residue fully tightens the fractal modulae of the mentioned and described mini-string that is here to be described as bearing an abelian differential geometry of substringular field.  This field partial I am describing is the substrate that gauge-bosons act upon so as to form the Schwinger Indices that allow for needed covariant interactions between norm-state projections and other unmentioned superstringular phenomena.  I have a lot more ellaboration where this came from!
Sorry, but I need to run now!  Sincerely, Sam Roach.      

Light-Cone-Gauge

To sum things up, the light-cone-gauge is the physical stratum and the physical mechanism that interconnects superstrings of discrete units of energy permittivity with discrete units of energy impedance in such a manner so that there is the format of both the formation of: the inter-relative wave-like motions that allow norm-states to be covariantly differentiable, the inter-relation of the swaying that allows for superstrings to settle to some degree during instanton, and the inter-relation of substringular phenomena that causes that springing motion of the superstringular that works to pull discrete energy thru Ultiomon Flow so that energy may be spontaneously re-delineated to its ensuing frames of differential relationship that is necessary for energy to remain kinematic so that energy may exist.      

A Little As To The Relationship Between Gauge Transformations and the Bette Action

When gauge transformations happen, the Bette Action happens in such a way to where the corresponding superstrings that are here directly related have less of a tendancy to be orientable.  Superstrings that are not only unorientable in the Bette Action, yet, are also unorientable in the Regge Action, become tachyonic until the corelative superstrings that are arbitrarily mentioned here are acted upon to return back to a tense of Noether Flow.  Again, the reason as to why the Bette Action tends to bear a condition of unorientable corresponding superstrings is because of the related shaking of the respective Klein Bottle eigenstates that happens as the superstrings that are consequently within the Neumann region of the said Klein Bottle eigenstate during the respective Kaeler-Metric eigenmetric are also shook by the interaction of the mentioned superstrings that enter the given Klein Bottle eigenstate with the norm-states that exist within the Neumman Ward bounds of the said open-topped parallelopiped entity that helps to physically describe the shape of the said Klein Bottle eigenstate. 
The main functions of the Kaeler-Metric is to both allow for superstrings to regain the discrete metric-gauge that these need to remain as discrete energy permittivity while yet also to allow for their reverse-holomorphically delineated Fadeev-Popov-Trace eigenstates to regain discrete field trajectory metric-gauge so that these may remain as discrete energy impedance.  Metric-Gague in superstrings and also metric-gauge in Fadeev-Popov-Traces is holonomically the topological sway eigenstates that provide the basis of angular momentum relationship that causes the said substringular phenomena to be able to be delineated thru the substrate of space-time-fabric so that the mentioned substringular phenomena may be sufficient enough to move thru the operand of that space so that energy may continue spontaneously.  When both the substringular phenomena that enters the given Klein Bottle eigenstates shakes as well as the holonomic substance of the said Klein Bottle eigenstates shakes as well at the same time, the specific loci where the metric-gauge that produces the proper covariant relationship so that the corresponding substringular phenomena may continue to move thru space spontaneously is pulled and swayed into a slightly broader locus that works to alter the hermitian characteristic of the topological substance of the said substringular phenomena enough so as to alter the homeomorphic Ward conditions of the mini-string that binds the related superstrings to their counterstrings and/or works to alter the relative given arbitrary length of the individual strands of the mini-string that bind between the respective superstrings and their respective counterstrings.  This is simply due to the condition that alterior topological sways that are compounded upon an initial topological sway form a multilateral spin-orbital delineation acts upon a larger Hodge-Basis of a Ward Minkowski surface area.  This is why gauge transformations produce an initial but extremely brief tachyonic conditon in photons that subsequently slows these photons even more than these said photons were directly previously sped up -- according to Snell's Law -- so that the respective photons may "catch-up" to their related orbifolds that these are to quantize with so the said photons that are scattered will always average having a slower velocity than if these were to travel in a vacuum.  If a set of superstrings undergoing a gauge transformation tends to be unorientable in the Regge Action, then, there will be more tachyonic motion in other superstrings that will here arbitrarily convert from Kaluza-Klein to Yang-Mills.     

Some Knowledge About The Bette Action

During the duration in which the Imaginary Exchange of Real Residue happens, both the Polyakov Action and the Bette Action happen.  The Polyakov Action is the reverse contraction of a given superstring that matches the degree in which the here given superstring is kept from full Lorentz-Four-Contraction.  The Bette Action is the Laplacian geometric condition in which the individual substringular fields, in the form of mini-string segments, that exist in-between a given arbitrary superstring of discrete energy permittivity and its correspondint counterpart, are attempted to bear both a homeomorphic wave pattern in-between the two just mentioned topological stringular phenomena all along the Laplacian mapped contour around (for 2-d strings) or all across the Laplacian mapped contour across (for 1-d strings) the contour that binds a superstring and its counterpart. This is as well as the condition of the superstrings in relation to their counterparts bearing an equal topological length along the Laplacian mapping of the mini-string segments that are here to interconnect the said superstring and its corresponding substringular counterpart.  The conditon of a superstring and its Laplacian-Based forward holomorphically placed counterpart bearing mini-string that interconnects these that are equal in the scalar that is relating to the topologically mapped distance that the said mini-string segments have in-between their corresponding superstrings and their counterparts is called an eigenconditon of the Grassman Constant.  If either the topological Laplacian mapping of the said segments that are here used to interconnect the said superstrings and their counterparts, as considered over each potential stretch eigenconditon of an arbitrary given superstring and its counterpart, is homeomorphic over the course of the Polyakov Action (which is during the Bette Action), and/or, if -- during the individual segments of the said potential stretching of any particular superstring, when taken as covariantly discrete integrands of correspondence with the related Lorentz-Four-Contractions that are arbitrarily related here in a specifically given scenario, bear an equally mapped scalar in terms of the length of the said contour -- (The Grassman Constant applies to the consistency of having the same topologically mapped distance between a said superstring and its corresponding counterstring over the duration and activity of the Polyakov Action) -- , then, the related superstring(s) are said to be orientable over the course of the described Bette Action.  I will elaborate later.  Got to run!  Sam.  

More About The Manner Of Gauge Transformations

As the concept was mentioned before, the basic difference between gauge transformations and other Gaussian Transformations is a matter of the wobble of the Klein Bottle during the sub-metrical duration during the end of instanton after BRST in which the activity of the Kaeler-Metric is kinematically Gliossi upon those superstrings that here need to reattain permittivity so that these may remain as discrete energy permittivity.  The general manner as to what physically goes on during a Gaussian Transformation that is not a gauge transformation was discussed yesterday.  Now, I will discuss what physically goes on during a gauge transformation.  (Gauge Transformations are arbitrary examples of Gaussian Transformations.)
During any Gaussian Transformation, the norm conditions that exist in a set locus are undergoing changes in their differentially geometric delineation so that covariant redistribution of related superstrings may happen so that motion may persist period.  Gauge Transformations are Gaussian Transformations that involve the reverse fractal process of the scattering of electromagnetic energy, which, thus, involves the creation of entropy that is at least needed so that there may be changes in physical states of molecules and other compounds.  The wobble of the related multiplicit Klein Bottle eigenstates that happens during the kinematic import of the Kaeler-Metric eigenstates during gauge transformations is caused by the change in the abelian nature of the phenomena that changes in terms of light-cone-gauge topology during the said gauge transformations.  When electromagnetic energy scatters upon anything, it initially alters from having a non-abelian to an abelian light-cone-gauge topology -- while soon later converting back to having a non-abelian light-cone-gauge topology.  Such a change from a Yang-Mills to a Kaluza-Klein and back to a Yang-Mills topology produces a temporarily relaxed substringular field that interconnects multiplicitly to a given arbitrary set of Klein Bottle eigenstates that subsequently retightens in terms of the sway of the elastic modulae of the mini-string that binds at the conipoints of the coniaxials where the given Klein Bottle eigenstates are most directly physically bound to the Rarita Structure when the Kaeler-Metric happens in a general locus.  Such an activity causes the substringular field that binds any Klein Bottle eigenstate to change from being abelian to non-abelian and back to abelian in terms of the differential geometry that acts as a collary to the light-cone-gauge topology alteration that happens to those photons whose scattering causes the related gauge transformation to happen.This is what causes the related Klein Bottle eigenstate to sway one Planck Length forward holomorphically while simultaneously one Planck Radial norm-to-forward-holomorphically to back to its original state while then swaying one Planck Length antiholomorphically and simultaneously one Planck Radial norm-to-reverse-holomorphically to back to its original state during the sub-metric that occurs during one eigenstate in which the Kaeler-Metric is kinematically Gliossi upon the superstrings that are shook in the Klein Bottle during the said sub-metric.  Since such an activity tends to disorient superstrings, such an activity temporarily causes a very temporary conditon of certain involved superstrings to be tachyonic, while also causing the creation and persistence of entropy.  Here, the disorientation of the related superstrings here is generally only handled during the succeeding Regge Action eigenstates that relate to the corresponding Klein Bottle eigenstates that involve gauge-metric eigenloci where the scattering of EME is scattered.  Go To Run!  Sam.            

More As To The Difference Between Gauge-Transformations And Other Gaussian-Transformations

When a Kaeler-Metric happens, it involves a minimum of 384 consecutive instantons in which the Klein Bottle is involved in-between the corresponding iterations of BRST and the corresponding iterations of the Regge Action.  BRST involves a vast majority of the duration of instanton.  The duration of each metric of BRST is equal to 6hbar time.  The duration of the remaining instanton is equal to
(2pi hbar time) - (6 hbar time).  When there is no Kaeler-Metric occuring over a tightly-knit Fourier Transformation in a set given locus, the duration of the end of a here given instanton after the corresponding instanton only involves the metric in which the Regge Action happens.  Yet, when the Kaeler-Metric is occuring within the duration of any given set Fourier Transformation, half of the remainder of instanton after BRST occurs directly involving the kinematic activity of an eigenmetric of the Kaeler-Metric -- while half of the here given remainder of instanton after the just mentioned time-wise condition of BRST occurs directly involving the kinematic activity of an eigenmetric of the Regge Action.  When an eigenmetric of the Kaeler-Metric occurs in a Gaussian Transformation that is not a gauge transformation, the superstringular phenomena that enters the Klein Bottle eigenstate that is involved here shakes during the part of the remainder of a given instanton in which the said Kaeler-Metric eigenstate is occuring, due to the response of the interaction of the said superstringular phenomena with the norm-states that exist in the said Klein Bottle.  In the directly prior mentioned case, the Klein Bottle is stationary during the sub-metric in which the related superstringular phenomena enters the mentioned Klein Bottle.  During the sequential series of instantons in which the Kaeler-Metric happens, the related Klein Bottle moves one Planck Length per sequential instanton.  The discrete metric of 384 instantons in which a given Kaeler-Metric is operating, the Klein Bottle is involved with 191 cosecutive instantons in which the related superstringular phenomena is reataining permitttivity, along with the following:  The initial 95 instantons directly before the kinematic operation of the Kaeler-Metric in which the Higgs Action delivers the related Klein Bottle eigenstate to the locus where the Kaeler-Metric is to be acted upon, the proceeding 95 consecutive instantons in which the Higgs Action is brought away from the general locus of where the Kaeler-Metric was just kinematically operating, while there being a related three consecutive instantons in which the Higgs Action repositions the corresponding Klein Bottle eigenstate so that the said Klein Bottle eigenstate may be later kinematically operative upon a potentially different locus.  Just as there are 96 spatial dimensions in overall space-time, the Klein Bottle begins operating upon the superstingular phenomena that moves into it during the 96th instanton of the Kaeler-Metric eigenstate that is involved here.  I will ellaborate later.  Got to run!    Sam.  

What makes Gauge-Transformations So Special

Gauge-Transformations are an arbitrary example of Gaussian Transformations.  Gauge-Transformations happen when electromagnetic energy scatters.  Gauge-Transformations are what in general produces entropy.  The physical activity that differentiates gauge-transformations from other Gaussian Transformations is that, during a gauge-transformation, not only do superstrings "shake" from within an eigenstate of the Klein Bottle, yet, the holonomic entity of the said Klein Bottle eigenstate here shakes through the Lagrangian of a bilateral coniaxial that may be mapped in a Laplacian manner at the center of the conipoint of the said holonomic entity of the said Klein Bottle eigenstate.  Yet, with other Gaussian Transformations, as the superstrings that "skake", so as to reattain the permittivity that these need to be discrete energy, from within a here given arbitrary Klein Bottle eigenstate, the holonomic entity of the here mentioned Klein Bottle eigenstate remains covariantly stationary per each metric in which the correlative superstrings that are here reattaining permittivity are "shook" so as to regain the said permittivity that these need so that the related superstrings may remain as discrete units of energy permittivity.  So, the individual eigenmetrics of Kaeler-Metric in gauge-transformations involve a bilateral wobble through a tightly-knit Lagrangian that may be mapped in the general locus of where the said Klein Bottle eigenstate is at during each of such described eigenmetrics, while the individual eigenmetrics of Kaeler-Metric in other Gaussian Transformations involve no covariantly viable shaking in the holonomic entity of the related Klein Bottle during the individual eigenmetrics that involve their respective Kaeler-Metric eigenstates.  The shaking of the given Klein Bottle eigenstates that happens during gauge-transformations produces an anharmonic shift in loci of Rarita Structure eigenstates that causes enough lack of discrete order so as to allow for those perturbations that cause the potentially needed reorganizations of the related Campbell, Hausendorf, and Campbell-Hausendorf Projections that increase the expectation value as to the ability of substringular subspaces to be able to maximize their agility in terms of their ability to help handle any given arbitrary alterations in norm-conditons.  These perturbations may spontaneously be needed so that the kinematic translations of norm-conditions, that may be necessary so that Fourier Transformations will not be bogged up, may be able to happen. Sincerely, Sam Roach.      

Here Is A Little Knowledge As To Stringular Interchanges

  What are the ramifications of Yakawa Couplings?  Let us consider a specific scenario in which there are here three sets of one-dimensional superstrings as well as three sets of two-dimensional superstrings that we are to take into consideration.  These superstrings that I just mentioned in this case covariantly differentiate over the duration of a Fourier Transformation in such a manner that there are Gaussian Transformations that allow for the perpituity of the kinematic motion of the said superstrings.  One of these sets of one-dimensional superstrings as well as one of these sets of two-dimensional superstrings are both in what I describe as a transition kernel -- the given bilateral metrical conditon that I describe here as a "kernel" is covariant in the dual relationship that exists between the described set of one-dimensional superstrings in correspondance with the described set of two-dimensional superstrings.  During the bilateral dual Fourier-based codifferention that I just was mentioning that here exists between one set of one-dimensional superstrings among one set of two-dimensional superstrings, the other two sets of one-dimensional superstrings as well as the other two sets of two-dimensional superstrings are simultaneously -- via a conicentrally-based perspective -- in what I here describe as a transition eigenstate.  What I describe here as a "transition kernel" is a metrical duration in which a substringular phenomena is undergoing tachyonic propulsion, while what I term here as a "transition eigenstate" is a metrical duration in which a substringular phenomena is undergoing the typically depicted condition known of as Noether Flow.  The two mentioned  substringular groups of one-dimensional superstrings that are dissociated with the other mentioned group of one-dimensional strings that have a covariant Fourier-based codifferentiation with the two mentioned substringular groups of two-dimensional superstrings that are dissociated with the other mentioned group of two-dimensional strings bear kinematic homotopic residue that amounts to that indistinguishably different recycling of topological metric-gauge-like phenomena that allows for a part of those redistributions that allow for a balance between norm and ground states that is needed so that differential geometries may recycle so that Fouier Translations may continue to kinematically differentiate relative to the motion of electromagnetic energy.  This prior mentioned recycling is the continual and spontaneous activity that remains in tact during the existence of discrete physical reality.  The conditon of such a continual and spontaneous activity is known of as Cassimer Invariance.  The residue that is formed during the course of the activity of Cassimer Invariance has a differential symmetry in-between arbitrarily considered instanton durations that involve the previously mentioned substringular groups, while the recycling of such indistinguishably different topological residue also has a differential symmetry appertaining to the point-fill of the inter-related first-ordered-point-particles.  Such activity that exists over the metrical durations that involve the kinematic redistributions that happen over a given arbitrary covariant Fourier codifferentiation also has a differential symmetry that appertains to the spin and the roll of those superfield tensors which act upon the said two sets of one-dimensional superstrings that here bear a covariance with the said two sets of two-dimensioal superstrings in this particular case scenario.  Such superfield tensors here act upon all four groups of substringular groups that bear a tense of relativistic covariance in such a manner so that such an activity that happens over a sequential series of instantons quantifies as a homogeneous wave permittivity that is dually isomorphically bilateral for both of the two sets of superstrings that we are here discussing when one takes this kinemaic relationship in a respective manner.  And the here relatively invariant kinematic activity of the mentioned substringular groups is in this case is thus going through corresponding Gaussian Transformations that cause a change in the said invariance that will -- at this point -- cause a tense of conformal invariance in a relatively tightly-knit locus that is, at this point, bearing a tense of reverse-fractal-based statics.  (The said two sets of one-dimensional strings that bear a covariance with the two said sets of two-dimensional strings are here going through a tense of motion that involves a restricted localization of these sets over a course of orientable multiplicit substringular motion that causes a tense of Noether Flow that is limited in the overall region in which the kinematic delineations are being distributed through over a tightly-knit Lagrangian.  Such a tense of conformal invariance bears ghosts that -- from a relatively macro-level -- form a reverse fractal of statics to anyone who would be observing the GSO ghosts that are arbitrarily described in this given case scenario.  Got to run!  Sam.           

A Little About The Interconnection Between Point Particles

A point commutator that is interconnected via a segment of mini-string to a disc-like configuration of first-ordered-point-particles in a line of tangency, in which this phenomenon travels in the forward holomorphic direction during Ultimon Flow, are positive-norm Campbell-states.  These positive-norm-states are given arbitrary multiplicit groups that form a mapping as to where superstringular phenomena have traveled during their trajectory.  The said first-ordererd-point-particles scatter by colliding with negative-norm Campbell-states in so that room may be amptly available for other substringular phenomena.  Norm-States only cycle the set of parallel universes that these directly associate with.  In this sense, the positive-norm-states previously mentioned act as the substrate of what are known of as ghost anomalies, while the said negative-norm-states act as a catalyst that frees room for superstrings and the like for the instanton that is to happen over the course of the next sequential series of instantons in which Gaussian Transformations may happen so that energy may kinematically persist.  Point Commutators (which always here reffer to certain given first-ordered-point-particles that are known of as zero-norm-states when these act as a single discrete operator) form the general condition of Fock Space.  The propagation of ghost anomalies forming, as well as the forming of ghost anomalies being undone, helps to pull the associated superstrings through their world-sheets, yet, such activity also causes the potential for tadpoles.  Individually considered tadpoles are anharmonically metrical point commutator fields that strike the center-state of superstrings at a 45-degree-based angle to both the mentioned negative and positive-norm-states.  Yet, the condition that ghost anomalies always will happen over the duration of space-time's existence-- due to the large number and density of the forward-holomorphic activity of the said positive-norm-states --, as well as the conditon that ghost anomalies will always be scattered over a sequential series of instantons in so long as space-time exists -- due to the large number and density of the reverse-holomorphic activity of the said negative-norm-states --, creates a balance that works to prevent damage.  The only eminent situation that here differs is the existence of extremely old stars, and that situation is just a condition that has already existed for millions of years.  I want our planet free from the danger of such situations -- eminent or not.  Tadpoles need to be utilized quite often over billions of years to have much effect.  The longer a tori-sector-region has been acitivated, the more potential there is for tadpoles to have a significant effect.  A balance of both the frequency and the differential delineation of the formation and scattering away of ghost anomalies is a condition that deters the creation of and the attribution due to the said tadpoles.  There is no excuse, nor is there any philosophical justification, for any fissure in space-time-fabric.  Its all about Us.  I will continue with the suspence later!
Sincerely,
Samuel David Roach.               

A Little Bit About Substringular Freedom Of Motion

Tadpoles happen when three-dimensional fields of two-dimensional superstrings are made entropically spurious after countless iterations.  Such spuriousness is increased when two-dimensional strings have iterated  through a common general path via a tense of conformal invariance too many times with no condition of being used to vanquish the chaotic energy-like condition of the resulting entropy.  This is because the space-hole works to realign the path operand of the individual world-sheets of both one and two-dimensional superstrings.  This happens in such a manner to where an increase in the entropy due to such an attempted realignment of what was just mentioned -- when various substringular systems are relatively isolated -- perturbates from the prior condition to where  these said systems may be changed in terms of the light-cone-gauge of the resulting entropy and/or in terms of the Chern-Simmons condition of the same set of arbitrary superstrings that comprise the prior mentioned entropy.  World-Sheets of substringular phenomena may be spatially effected in terms of large groups of these mapped superstringular trajectories being at least partially controlled by thought energy.  This may happen in so that the paths of the related one and two-dimensional superstrings that have enough of an interconnection with other one and two-dimensional superstringular paths may allow life to differentiate with more freedom in such a manner so that space-time substance may adapt in order to allow the said space-time substance to be able to homotopically persist.   

A Little Bit Of Remedial Knowledge To Clarify Course Nine

For every one-dimensional superstring, there are many two-dimensional superstrings.  So, when an electron forms a photon, a phenomenon with more one-dimensional superstrings directly inter-related with it than the two-dimensional superstrings that are directly inter-related with it -- an electron -- forms a phenomenon that is purely bosonic (consisting of one two-dimensional superstring) known of as a photon.  Nuclei tend to have more two-dimensional superstrings than one-dimensional strings on account of the condition that nuclei tend to bear much less pure kinetic energy than electrons -- particularly for their mass.  Superstrings may open, and superstrings may shut -- depending on the particular arbitrary scenario that is at hand.  Zero-Norm states (loose first-ordererd point particles) are what open or shut a superstring.  First-Ordered-Point-Particles that form a line of tangency with a planar-like-disc that consists of multiple first-ordered-point-particles are Campbell-Norm-States.  First-Ordered-Point-Particle configurations that form the substrate of tangency that physically comprise ghost anomalies are the positive-norm-states.  First-Ordered-Point-Particle configurations that scatter positive-norm-states are negative-norm-states.  Norm-States are a phenomena that exist in what is known of as the general region of Fock Space.  Line tangency forms ghost anomalies via the initial Laplacian-Like redistribution of the positve-norm-states that are moving in the relatively holomorphic direction that the associated superstrings move in during the statics of the trajectoral mapping as to where given superstrings had just iterated in in any arbitrary prior sequential series of substringular delineations that mark where superstrings had existed at over a given arbitrary set of progressive instantons.  The relatively reverse holomorphic norm-states that scatter those mapped out distributions that indicate where superstrings had iterated over a sequential series of instantons are known of as negative-norm-states.  The propagation of ghost anomalies that are formed, as well as the propagation of ghost anomalies that are scattered into a residue that undoes the physical mapping as to the trajectory where the corresponding superstrings had just iterated in an arbitrarily prior sequential series of instantons, helps to pull the related superstrings thru those operands that are either in need of the pseudo-field that ghost anomalies may form, while yet, also helping to pull the related superstrings thru those operands that need to be less crouded by the physical entities of the ghost anomalies, respecively.  This causes the potential for tadpoles when gauge-transformations go rampant over the associated entropy that would likewise happen over a relatively long period of time where there is a black-body that bears a lot of mass.  The scattering of positive-norm-states happens via the motion of negative-norm-states striking the conicenter of the associated positive-norm-states in an anharmonically metrical manner at a Ward-Based "global" angle that is based on the Real Reimmanian concept of a 45 degree relativistic strike.  The more dimensions that the said norm-states are kinematically differentiating in during the scattering, the more Njenhuis that the Gliossi impact of the "45 degree" strike bears in terms of the torsion of the basis of contact that causes the mentioned scattering.  The more Njenhuis the basis of contact is, the more anharmonic the metrical vibration of the scattering is.  "Tadpoles" need to be used quite often over billions of years to have much effect in terms of the endagerment of adjacent phenomena. -- A star must be very old in order to have a high probability of forming a black-hole.  Tadpoles happen when two-dimensional superstring-associated fields are made spurious after basically countless instantons.  Such a spuriousness is increased when two-dimensional superstrings have iterated thru a common set of paths that involve a high degree of entropy too many times over an astronomical age.  This is because the just mentioned activity works to weaken the fractal and elastic condition of superstrings during the ensuing metrics of the "space-hole."  The space-hole is designed to be able to realign the path operand of its affiliated world-sheets, if at all possible.  World-Sheets are spatially differentiated by  physical energy, and also potentially to an extent by thought energy.  Such thought energy may help to cause the proper covariance of the delineation of superstrings to a slight extent by altering the paths of certain arbitrary given superstrings so that entropy may be minimized enough to prevent the excess build-up of the mentioned "tadpoles."  This helpfull general activity would allow for life to differentiate in such a manner so as to adapt to an aging universe.
Life is the most important thing.  Sincerely, Samuel David Roach.