Alteration In Modulus Of Net Gauged-Action -- Gauge-Transformation

 When the net gauged-action of a Hamiltonian Operator, is to alter in its modulus, this general type of a Ward-Cauchy-Related operation, in the arena of superstrings, will tend to work to form, what may be termed of, as being a gauge-transformation. I WILL CONTINUE WITH THE SUSPENSE LATER! CONTINUED LATER! SINCERELY, SAMUEL DAVID ROACH. (1989).

Recursively Iterative Tense Of Gauge-Transformation -- Recursively Smooth Ricci Flow

 The more recursively iterative that the tense of a sequential pattern of Noether-Based gauge-transformation is to be, for a a respective kinematically displaced phenomenon of topological manifold, that is here to be in the general process of undergoing the Fourier-Transformation of a Lagrangian-Based motion, that is here to be directly associated with the simultaneous transversal and radial spatial transference of such a stated topological manifold, to where such an inferred manifold of phenomenology, is here to exist as a given arbitrary uniquely distinct respective mass-bearing cohesive set of discrete energy quanta, to where it will thereby often follow, that the directly associated consistent flow, of the kinematic motion of the inferred "team" of mass-bearing energy, will consequently tend to be delineated, in such a general manner, to where it will thereby have the general tendency, of working to exhibit a recursively smooth Ricci Flow. I WILL CONTINUE WITH THE SUSPENSE LATER! SINCERELY, SAM.

More Spin-Orbital Tensors -- More Entropy Produced

 The more spin-orbital tensors, that are here to be directly associated, with the kinematic rotational motion of a cohesive set of discrete energy quanta, the more entropy that will consequently tend to be produced, when a photon, (which is of electromagnetic energy), is to scatter upon the topological stratum, of the immediately eminent externalized core-field-density, which is of such a said cohesive set of discrete energy quanta, that is in the process by which there is here to be the proximal local presence, of the activity of one general type of a consideration, that may be thought of as being a "gauge-transformation." 

P.S: In my model, what I mean by a "gauge-transformation," may potentially mean one of two different things -- depending upon the context of what is here to be logically conveyed.  (As in "homonyms") Let me explain these two different  meanings that I have ascribed to the idea, as to what a "gauge-transformation" is.:

1) Any time that the eminent structural delineation/behavioral aspects, that are here to be of the nature of the physical "allotment" of a given arbitrary light-cone-gauge eigenstate, is to change, or transform, -- this general type of a behavior, may often tend to be thought of as being, of a "gauge-transformation."

2) Any time that electromagnetic energy is to scatter upon a phenomenology, -- to where there is here, to be a general type of a superstring-related process, by which that cohesive set of one or more discrete energy quanta, that had just been scattered upon, are then to spontaneously be brought into such a "situation," to where this inferred "team" of energy, is to ensue in so as to then become Gliosis to the Kahler-Metric, -- that such a general type of a superstring-related process, of which is often to tend to be associated with when a set of one or more cohesive light-cone-gauge eigenstates are to alter/change, in there eminent structural delineation/behavioral-related aspects, -- this may be another type of a way, of working to describe, what may be thought of as being, of the nature of acting as a "gauge-transformation." 

This should make things a little bit clearer, I Hope. Sincerely, SAMUEL DAVID ROACH. (1989).

Some Stuff As To Superstringular Orientation

A superstring that is orientable differentiates kinematically via Noether Flow.  A superstring that is not orientable differentiates kinematically via a tachyonic flow.  A superstring is orientable -- when the substringular field eigenstates that are first-order and supplementally norm between a given superstring and its corresponding counterstring, are trivially isomorpphic in terms of the connections in-between the associated superstring and its corresponding counterstring,-- as caused by the Bette Action, and if the delineatory amplitudes of these said connections have the same scalar distribution, when considering all of the said first-order substringular field eigenstates, even if the Hodge distribution among the said field eigenstates is not homogeneous and therefore not integrably hermitian, during the Laplacian condition of the given instanton in which the associated Bette Action is occurring through its described gauge-metric.  If a superstring is not orientable during the Bette Action, the superstring described will attempt to become orientable during the subsequent gauge-metric of a given Regge Action, via a Regge Slope that "totters" the associated superstring, in an attempt to obtain the multiplicit trivial isomorphism and a common homogeneous and delineatory amplitude, that bears a supplementally norm abelian nature that retains the Noether Condition of the said superstring's wave-tug.  (This is via a simultaneous internal push-and-pull that is exterially projected along the Ultimon.)  If a superstring is still unorientable during the Regge Action, then the associated superstring becomes tachyonic.  This is an example of how a lack of substringular super-symmetry may effect the differential operation of that superstring. over a simple Laplacian Transformation, which, if such a condition is integrable over a sequential series of iterations that is non-trivial gauge-metric-wise, this will then form a Fourier Transformation that involves a superstring -- that is tachyonic and thereby perturbative, relative to its general condition of Noether Flow.  Such a perturbation effects the matrix of the delineatory index of the involved orbifolds, that are directly effected by this tachyonic multiplicitly integrable distribution.  Since the anharmonic multiplicit redistribution of a kinematically unorientable superstring flows differently then the surrounding Noether Conditions, and Noether Conditions are the kinematic delineatory means of maintaining the norm conditions, that work to allow for a sustained covariant Gaussian Symmetry, the Fourier Transformation involved with a tachyonic flow, will produce change in Gaussian Symmetry -- either via a regular Gaussian Transformation or via a gauge-transformation, the latter of which is the substringular cause of entropy.  Sincerely, Sam Roach.

Gauge-Transformations That Work To Produce Heat

Whenever a set of gauge-transformations, works to help at producing an anharmonic vibration of molecules -- this will always tend to be a case, in which the scattering of light upon a Calabi-Yau manifold --  is to be in the process of working to form a certain scalar amount of heat or infrared energy,  over time.
I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.

Gauge-Transformations And Kahler-Metric

A Gauge-Transformation is that special case -- as to when a set of one or more superstrings that are of one proximal locus, are Gliosis to the Kahler-Metric -- in which there is the direct involvement of the scattering of electromagnetic energy.
I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.

Simultaneous Dual Gauge-Transformations

Let us initially consider a set of orbifold eigensets -- that work to comprise the holonomic substrate of one given arbitrary molecule.  Let us next consider the molecular condition, that any set of one or more atoms -- namely in this case, here, a molecule, -- is going to bear at least a certain scalar amplitude/scalar magnitude, of a tense of both an internalized and an externalized vibrational-oscillatory-based mode, as such a molecule is to here be undergoing its so-eluded-to tense of a Majorana-Weyl-Invariant-Mode, at its proximal local reference frame, over an allotted respective period of time.  As any given arbitrary molecule vibrates -- such an oscillation-based mode, will tend to work to form a certain Calabi-Yau scattering of the electrostatic eigenindices of that molecule, in so as to help to allow some of its correlative component electrons, to undergo the Fujikawa Coupling -- in so as to help at working to form proximal localized heat energy.  Often, especially with luminescent molecules, -- the proximal local presence of infrared or heat-based photons, will help to encourage that general genus of the Fujikawa Coupling, that is to here work in the formation of white or visible light.  So here, as that general genus of a gauge-transformation is to happen, in so as to work to form infrared or heat-based photons, there is to then, as well, be the occurrence of the spontaneous activity of the general genus of a gauge-transformation to happen, that will work to form photons of visible light.  In this manner, that general genus of activity, that works to form the multiplicit gauge-transformation that is related to the formation of heat energy, is to here, with luminescent-based molecules, to work to form the multiplicit gauge-transformation that is related here to the formation of visible light energy.  Often, a heat differential, that is to be applied to the here respective given arbitrary luminescent set of molecules, is what will work to set-off the so-eluded-to gauge-transformation-based response.
I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.

More As To Gaussian Transformations Versus Gauge-Transformations

With a Gaussian Transformation that is here to not be a gauge-tranformation, as the directly corresponding discrete energy quanta that are to here be most Yukawa to the correlative Kahler-Metric manifold -- as the correlative directly corresponding holonomic substrate of the pertinent Klein Bottle eigenstate, that is to be made Gliosis to the just mentioned discrete energy quanta, is to shake in a significant manner, this shaking is to only happen in the general direction of the holomorphic directorial-based Lagrangian-based Hamiltonian operand, that is in the path of holomorphic wave-tug of the correlative set of discrete energy quanta, where the correlative set of superstrings of discrete energy permittivity are to ensue, right after the then metric-wise iteration of BRST is to then be happening.  Yet -- with a Gaussian Transformation that IS here to be a gauge-transformation, as the directly corresponding discrete energy quanta that are to here be most Yukawa to the correlative Kahler-Metric manifold -- as the correlative directly corresponding holonomic substrate of the pertinent Klein Bottle eigenstate, that is to be made Gliosis to the just mentioned discrete energy quanta, is to shake in a significant manner, this shaking is to happen in both the general direction of the holomorphic directorial-based Lagrangian-based Hamiltonian operand, as well as in the Njenhuis-to-holomorphic directorial-based Lagrangian-based Hamiltonian operand, that is in the path of the holomorphic wave-tug of the correlative set of discrete energy quanta, where the correlative set of superstrings of discrete energy permittivity are to ensue, right after the then metric-wise iteration of BRST is to then be happening.
I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.

Part Two As To Consecutive Chern-Simons Singularities

Let us here consider an orbifold eigenset, that is moving in the relative forward-holomorphic direction.  Let us next consider that the just mentioned orbifold eigenset, is to all of the suddenly spike into what is to here be the relative reverse-Njenhuis to forward-holomorphic direction -- to where this said activity is to here, work to form a Lagrangian-based Chern-Simons singularity -- that is of a genus of one.  Let us next say that the just mentioned orbifold eigenset, is to ensue, in so as to just about immediately spike again, into a Fourier-based activity that is to all of the sudden -- veer into what is to be the ensuing motion of that self-same orbifold eigenset, into what is now to be the relative reverse-Njenhuis to forward-holomorphic direction.  Again, this general type of a Fourier-based activity, is to here work to form another Lagrangian-based Chern-Simons singularity -- that is again to be of a genus of one.  This general type of activity -- that is to here involve the cohomological mappable-tracing of two consecutive Lagrangian-based Chern-Simons singularities, of which are to happen almost immediatley ensuing Lagrangian-based spikes -- will tend to often work to form what will here almost ensuredly work to form an antiholomorphic Kahler condition.  Such an antiholomorphic Kahler condition, will here tend to initiate the proximal localized condition -- of what here may called the Wick Action, via a group-related metric that is called the Kahler-Metric.  The Fourier-based activity of the Kahler-Metric, tends to always work to ensue the presence of the activity of what may here be termed of as a Gaussian Transformation.  A gauge-transformation is always an example of a genus of a Gaussian Transformation, yet, not all Gaussian Transformations are of  the general nature of what I have just termed of as a gauge-transformation.
I will continue with the suspense later!  To Be Continued! Sincerely, Samuel David Roach.

Introductory Stuff About The Scattering Of Light

Whenever a beam of electromagnetic energy is to strike a phenomenology of mass, in a Gliosis-based manner, over time -- there will tend to be a certain amount of entropy that will here be formed by that general Fourier-based differentiation, that is of the activity of the so-eluded-to collision of the set of one or more photons, that are to here make a direct impact upon mass-bearing superstrings of discrete energy quanta, that will here work to help to form a tense of a Gaussian Transformation -- that may here be called a gauge-transformation.  A gauge-transformation is that general tense or genus of a Gaussian Transformation, that is formed as a gauge-metrical-based Hamiltonian operation, by which those so-eluded-to entropic-based eigenindices, that  are thence to here be formed by the so-eluded-to general activity of electromagnetic energy, are to have here just been struck by another physical phenomenology, to where this may bear an added tense of activity, over the course of the  needed replenishment of discrete quanta of energy -- that is to here be in the process of regenerating back their fractals of discrete energy -- so that discrete energy may be able to both persist and exist, over time.  I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.

An Example Of A Calabi-Yau Genus Of Interaction

Let us consider an initial orbifold eigenset that is comprised of superstrings of discrete energy permittivity, that is moving through a discrete unitary Lagrangian -- in what is here to be considered as to be moving in the relative holomorphic direction. Let us next say that the said orbifold eigenset is to then collide with a relatively motionless set of orbifold eigensets -- in such a manner in so that the initially so-stated orbifold eigenset is to then bounce into what may here be considered as the relative reverse-holomorphic direction.  Let us consider here that both the initially mentioned orbifold eigenset and the so-eluded-to conformally invariant set of orbifold eigensets that it is to collide with, are all comprised of mass-bearing superstrings of discrete energy permittivity.  Let us, as well, consider here that the initially mentioned orbifold eigenset and the said conformally invariant set of orbifold eigensets that it is to collide with -- will, upon the course of the so-eluded-to Gliosis-based contact, act in so as to work to form a relatively mild yet existent amount of heat energy, in the process of their interdependent contact -- due to the relatively slight amount of friction that is to happen in the process of their so-mentioned impact.  The scattering of the so-stated heat energy that is formed -- in part by the contact of the two so-eluded-to tenses of holonmic substrate, will then work to form a Calabi-Yau interaction that will here work to involve a gauge-transformation.
To Be Continued!  Samuel David Roach.

Part Seven of Session Two of Course 19 -- The Klein Bottle and Orbifold Differentiation

When there is a Gaussian Transformation that is happening during the period in which the Kaeler Metric is going on -- in such a manner in so as to act as a gauge-transformation -- there is one genus of a difference between this general category of a Gaussian-based Transformation and the rest of this general category of a Gaussian-based Transformation.  This one genus of a difference, is that, during a gauge-transformation,  the directly corresponding Klein Bottle eigenstate of any one individual specific respective given arbitrary cite, in which such a Kaeler Metric is undergoing its general format of activity -- will work to bear an additive side-to-side torsioning,  that would here be applied to both the relatively reverse holomorphic end and the relatively forward holomorphic end of such a so-stated respective given arbitrary Klein Bottle eigenstate.  This general genus of activity, will then tend to increase the tendency of a relative lack of such a holonomic substrate as a given arbitrary Klein Bottle eigenstate -- from appearing to  be anything that is even similar in morphology to an open-top parallelepiped, in this case.  So, when one is to work to extrapolate the mappable tracing of any respective given arbitrary Klein Bottle eigenstate, that is here to be undergoing a correlative gauge-transformation -- there will be an additional torsional-based cohomological-based twisting of the here directly corresponding ghost-based indices -- to where the resultant homotopic-based physical memory of both the existence and the activity of such a so-stated Klein Bottle eigenstate, will give the appearance of a somewhat membronous morphology, that, in a way, may appear as looking at the trippy "innards" of a microscopic organism.  Most Gaussian Transformations are gauge-transformations, as I will explain later in the future.  To Be Continued!  I will continue with the suspense later!  Sincerely, Sam Roach.

A Tad Bit Of An In-Depth Discussion

A field that is tachyonic is a perturbative field that becomes divergent from an initial state of a relative tense of conformal invariance -- or, from an initial condition of Noether Flow -- into a flow that involves a combined Real and Njenhuis given arbitrary format of tensors that work to inter-bind the eluded to phenomenon that here becomes tachyonic. This process ends-up resettling the said phenomenon at a relatively distant locus, in a manner that involves a format of a re-convergence back into Noether Flow, once such a phenomenon settles, for the said phenomenon that had here become tachyonic previously. Either way, any tachyonic field will end-up forming a Wick Action eigenstate in so as to produce an ensuing Gaussian Transformation. So, any tachyonic field will involve a Cambell-Hausnedorf-Projection eigenstate that will pull upon a Hausendorf-Projection known of as a Wick Action eigenstate --  in a manner that acts as a correlary to the genus of activity that pulls a Wick Action eigenstate into a Landau-Gisner-Action eigenstate -- due to the indirect influence of the directly associated light-cone-gauge eigenstates upon the local Rarita Structure, as a given arbitrary phenomenon is acting in a tachyonic manner. The said Landau-Gisner-Action eigenstate then acts upon a Campbell-norm-state that works to physically leverage a Klein Bottle eigenstate via a holonomic substrate known of as a Higgs Boson eigenstate, in so as to pull the just mentioned Klein Bottle eigenstate into the general locus in which certain given arbitrary superstrings that need to undergo a Kaeler-Metric eigenmetric may be able to do so.  The Kaeler-Metric is the duration in which superstrings are differentiated upon in such a manner to where these corresponding superstrings may be able to undergo a Gaussian Transformation.  The format of the manner as to how the Klein Bottle eigenstates are put together is called the Schotky Construction.  When the Ward-Caucy-based plane of superstrings that are to enter a Klein Bottle eigenstate falls into the said Klein Bottle in a hermitian manner (in a flush manner), then, the directly related Gaussian Transformation is not a gauge-transformation.  So, when the Ward-Caucy-basd plane of superstrings that are to enter a Klein Bottle eigenstate bears Chern-Simmons singularities upon entry to the respective Schotky Construction (when the eluded to entry is not flush), then, the directly related Gaussian Transformtion is a gauge-transformation.  Another way of looking it is, when a Klein Bottle eigenstate is relatively stationary or static during a sub-metric of a directly related Kaeler-Metric, then, the directly related Gaussian Transformation is not a gauge-transformation.  Yet, when a Klein Bottle eigenstate wobbles at all beyond its basic static core vibration, then, the directly related Gaussian Transformation is a gauge-transformation.  The need for gauge-transformations when E.M. scatters is one given arbitrary case of such an activity. (Although light that scatters moves slower than in a vacuum, on the whole.) The activity of gauge-transformations not only allows for those Gaussian Transformations that involves that re-assortment that is necessary for E.M. to be propagated without disruption, yet, such activity also, ironically enough, works to allow for for the creation of entropy. Entropy is needed for the neccesary changes in physical states. To Be Continued! Sam Roach.

Part Three of the Test Solutions to Course 14

6)  When the abelian nature of a given arbitrary light-cone-gauge eigenstate is maintained over a successive series of iterations of group instanton, such a condition is known of as gauge-invariance.  So, this condition exists if a Kaluza-Klein light-cone-gauge topology remains as a Kaluza-Klein light-cone-gauge topology, or, if a Yang-Mills light-cone-gauge topology remains as a Yang-Mills light-cone-gauge topology.

7)  When the abelian nature of a given arbitrary light-cone-gauge topology changes from either an abelian format to a non-abelian format, or, from a non-abelian format to an abelian format, then, this is called gauge-transformation.

8)  When the interconnectivity of a locus of topological substrate is maintained in terms of the relative general cohomological binding cites, then, this is known of as topological invariance.

9)  When the interconnectivity of an altered locus of topological substrate is altered in terms of the relative general cohomological binding cites, then, this is known of as topological transformation.

A Little Bit Of Help As to the last part of session 5 of course 14

The duration of the space-hole is ((2pi-6)*(10^(-43)/2pi))Iseconds.  We only tend to notice the duration of the successive iterations of group instanton.  Group instanton is the series of Real-basedd 10^(-43)second intervals that we tend to perceive of.  The light-cone-gauge eigenstates ideally are connected to the reverse-to-holomorphic side of their directly corresponding superstrings of discrete energy permittivity.  Yet, this situation happens to be only true all of the time during each individually taken discrete substringular increment of group instanton.  For superstrings of discrete energy permittivity that are positioned differently  from such a polarized positioning, the light-cone-gauge eigenstates are angled in a Njenhuis-based delineatory manner from where these are positioned at during a metric-based local iteration of group instanton.  This happens during the generally unnoticed duration of Ultimon Flow.  The format of such angling always counters the angling that the corresponding counter strings and their directly corresponding Planck-like phenomena happen to be off of -- by the inverse of the given arbitrary degree of Ward-Caucy polarization, in such a manner that is necessary for the said initially mentioned superstrings -- along with their correlative Planck-like phenomena -- to be able to flow holomorphically through the Ultimon.  This invariant angling compensation of the light-cone-gauge eigenstates that allows the said eigenstates to flow through the Ultimon is called gauge-invariance.  The previously eluded to angling that the correlative mini-string segments perform to allow subtringular phenomena to be able to both make-room for spontaneous continued motion via changes in kinematically physical norm-conditons, and, to form enough entropy in so as to allow for changes in physical states to be able to exist, is called gauge-transformation.

About the Metrical Activity That Allows For Permittivity

                                   


                                   
Phenomena has to move to exist. Metric-Gauge is the topological Laplacian Poincaire Ward conditions that integrate through the Fourier Conditions of substringular multiplicit group metrics that must exist in order for superstrings to have the ability to move through space and therefore be the energy that is necessary for reality to exist. Superstrings are the discrete units of energy permittivity. Permittivity is the ability of phenomena to continue to move through space. If discrete units of energy could not move, energy would cease to exist. Without energy, there would be no light, nor would there be any mass. When superstrings circle the ultimon many, many times, these phenomena (superstrings) lose some of their permittivity. The process that causes superstrings to regain the permittivity that these need in order to remain energy so that energy may exist is known as a Gaussian-Transformation, which is usually a gauge-transformation. The initial situation is that gauge-transformations eventually lead to entropy. Yet, there is a way of limiting gauge-transformations to those that just allow for substringular permittivity without allowing for excess entropy. Entropy is essential for at least the change of physical states. I will say no more of this. The reason that energy started and still persists comes down to the existence of the Higgs Action. The Higgs Action is the main operator that allows for Gaussian Transformations. See my post of the leverage of the Higgs Action on my blog

samsphysicsworld@blogspot.com. I am doing this out of a love for mankind.

I am very blessed to have the friends that I have.

Sincerely,

Samuel

A Little Bit About Changes In Symmetry

A superstring that is orientable differentiates kinematically via Noether Flow. A superstring that is not orientable differentiates kinematically via a tachyonic flow. A superstring is orientable when the substringular field eigenstates that are first-ordered and supplementally norm between a given superstring and its corresponding counterstring are trivially isomorpphic in terms of the connections in-between the associated superstring and its corresponding counterstring as caused by the Bette Action, and if the delineatory amplitudes of these said connections have the same scalar distribution when considering all of the said first-ordered substringular field eigenstates, even if the Hodge distribution among the said field eigenstates is not homogeneous and therefore not integrably hermitian during the Laplacian condition of the given instanton in which the associated Bette Action is occurring through its described gauge-metric. If a superstring is not orientable during the Bette Action, the superstring described will attempt to become orientable during the subsequent gauge-metric of a given Regge Action via a Regge Slope that "totters" the associated superstring in an attempt to obtain the multiplicit trivial isomorphism and a common homogeneous and delineatory amplitude that bears a supplementally norm abelian nature that retains the Noether Condition of the said superstring's wave-tug. (This is via a simultaneous internal push-and pull that is exterially projected along the ultimon.) If a superstring is strill orientable during the Regge Action, then the associated superstring becomes tachyonic. This is an example of how a lack of substringular super-symmetry may effect the differential operation of that superstring over a simple Laplacian Transformationm which, if such a condition is integrable over a sequential series of iterations that is non-trivial gauge-metric-wise, will form a Fourier Transformation that involves a superstring that is tachyonic and thereby perturbative relative to its general condition of Noether Flow. Such a perturbation effects the matrix of the delineatory index of the involved orbifolds that are directly effected by this tachyonic multiplicitly integrable distribution. Since the anharmonic multiplicit redistribution of a kinematically unorientable superstring flows differently then the surrounding Noether Conditions, and Noether Conditions are the kinematic delineatory means of maintaining the norm conditions that allow for a sustained covariant Gaussian Symmetry, the Fourier Transformaion involved with a tachyonic flow will produce change in Gaussian Symmetry either via a regular Gaussian Transformation or via a gauge-transformation, the latter of which is the substringular cause of entropy.                


Sincerely, Samuel David Roach. samsphysicsworld@blogspot.com.