Hamiltonian Operator -- Escalating Clifford Expansion -- Correlative Facilitation Of Escalating Euclidean Expansion

 When the proximal local Clifford Expansion, that is of the Lagrangian-Based motion, of a given arbitrary kinetically transferred Noether-Based mass-bearing Hamiltonian Operator, is to smoothly escalate, in a general heuristically hermitian manner, when this stated general process, is here to be occurring, under the general Ward-Cauchy-conditions, of the directly associated proximal local influence, of a given arbitrary homomorphically delineated anti gravitational field, this general type of a superstring-related situation, may often tend to work to facilitate, the correlatively eminent respective spontaneous escalation, of an accompanied Euclidean Expansion, when this is in terms of the general mannerism of kinematic Lagrangian-Based flow, of which the earlier inferred mass-bearing Hamiltonian Operator to be exhibiting the display of, over the directly corresponding respective durational span, of a correlative sequential series of group-related instantons. 'TILL NEXT TIME; ON THIS BLOG! TO BE CONTINUED! SINCERELY, SAMUEL ROACH. (1989).    

Transference Of A Holonomic Metric-Gauge Eigenstate

 When a holonomic metric-gauge eigenstate, is to work to bear a tangential spatial propagation, over the relativistic covariant co-differentiable span, of a sequential series of instantons, this will have a tendency of being eminently related, to the spatial transference of an energy-related increment, through a correlative Lagrangian, over a respective duration of time. TO BE CONTINUED! SINCERELY, SAM ROACH. (PINCKNEY, MICHIGAN, HIGH SCHOOL CLASS OF 1989).

What Facilitates The Formation Of Cohomology

 The resultant strain of the quantization of the del of the net gauged-action, of an energy-related eigenstate in the superstring-related realm, when imparted upon the correlative respective Hamiltonian Operator, through a correlative respective Lagrangian, as taken over the Fourier-Related-Progression of a sequential series of group-related instantons, is a key factor, as to what works to facilitate the formation of the general phenomenology of Cohomology. I WILL CONTINUE WITH THE SUSPENSE LATER! SAM ROACH.

A Refinement -- As To Metric-Based Chern-Simons Singularities

 When a cohesive set of one or more discrete energy quanta, is to alter in its dimensional-related pulsation, As this is here to be considered, -- over a sequential series of group-related instantons -- this general process of a superstring-related activity, -- as taken at the locus at which such an alteration in the dimensional-related pulsation is here to be occurring, is thence to be indicative, of the proximal local presence, of a tense of a metric-based Chern-Simons singularity. TO BE CONTINUED! SINCERELY, SAMUEL ROACH. (1989).

Some Definitions -- Appertaining To My Model Of String Theory

 Hamiltonian Operator -- 1) The overall energy of a system.

                                          2) The overall zero-point energy of a system.

Lagrangian -- 1) The actual motion of a discrete quantum of energy.

                      2) The actual motion of a cohesive set of discrete energy quanta.

                      3) The actual motion of a Hamiltonian Operator.

Hamiltonian Operand -- The proximal local physical Substrate, of which a Hamiltonian Operator is to be traveling through, over the course of a proscribed duration of "time."

Lagrangian-Based Path -- The sequential series of the mappable-tracing, of a Hamiltonian Operand.

Hamiltonian Operation -- 1) The functional tendency of action, of which a given arbitrary Hamiltonian Operator is to incur, upon its respective Ward-Cauchy-Related environment.

                                         2)The actual kinematic activity of a Hamiltonian Operator.

                                         3) The actual gauged-action of a Hamiltonian Operator.

Time -- The successive series of covariant group-related instantons. 

I encourage Anyone to provide input -- as to your ideas, appertaining to this blog! Sincerely, SAM.

                      

Outward Exertion Of External Field Of Orbifold Eigensets

That general outward moving propagation-related exertion of the external field, that is of any one given arbitrary Noether-based orbifold eigenset, tends to be the main manner, in which the discrete tense of the holonomic substrate -- of that general force that may be conveyed of here as being correlative to the E(8)XE(8) stringular oscillation-based tendency, -- is consequently to bear a respective propagation into the general realm of the Rarita Structure, in so as to often tend to help to form an influence upon all of the other 7 main forces of nature, over the duration-related processes of the sequential series of group-related instantons. Sincerely, Samuel David Roach.

Ideas And Time

Even though time is actually the multiplicit duration of the sequential series of group-related instantons, time is Equivalent to acting as a Yukawa Coupling between ideas and inertia. Sincerely, Sam Roach.

When The Polyakov Action Is Not Perturbative

Let us initially consider a given arbitrary orbifold eigenset, of which is here to be comprised of by the presence of mass-bearing superstrings of discrete energy permittivity.  The multiplicit Polyakov Action of these composite superstrings, is here to bear a respective tense, that is currently here (over a correlative evenly-gauged Hamiltonian eigenmetric) to not be of a perturbative nature.  During the course of such an inferred correlative sequential series of group-related instantons (which is here to be over the course of the earlier implied evenly-gauged Hamiltonian eigenmetric), the composite superstrings of discrete energy permittivity -- are here to each, when individually taken, to work to bear an iterative tense of the Polyakov Action, that is here to not be in the process of being perturbated.  Since the correlative tense of the Polyakov Action, that is here to be applied to the covariant fluctuation of the topological statum of such implied strings, is here to be maintained in its scalar amplitude, for the effectual import of the correlative conservation of homotopic residue of this particular case, when this is here to be taken in terms of the directly corresponding attribute, by which the correlative Lorentz-Four-Contraction that is here to be applied to the eminent condition of such said strings, is here to currently be maintained, to where this will consequently work to mean, that the relative motion of these said composite strings, when in their relationship to both the presence and the motion of electromagnetic energy, will consequently work to be maintained.  Furthermore -- this will consequently mean, that the directly corresponding i*PI(Del) Action will then, at this point in codifferentiable duration, act, in so as to tend to Not be eminent in its kinematic translation, over the so-eluded-to proscribed duration of time, in which the said respective tense of the Polyakov Action is here to Not be in the process of altering for these said superstrings of discrete energy permittivity, that are here to work to comprise the earlier mentioned orbifold eigenset of such a given arbitrary case.  To Be Continued!  Sincerely, Samuel David Roach.

Tense Of Lagrangian And Kahler-Based Quotients

Let us initially consider three different mass-bearing orbifold eigensets, that each work to exhibit the same number of spatial dimensions -- to where each of such said eigensets, is here to both bear the same scalar magnitude of mass, as well as there here to be the Ward-related condition, that each of such said eigensets is to be traveling at the same relativistic velocity, -- from the vantage-point of a central coniaxion.  One of such orbifold eigensets is here to work to bear a unitary Lagrangian, in the course of the process of its motion through its directly corresponding Hamiltonian operand.  Another of such orbifold eigensets is here to work to bear a binary Lagrangian, in the course of the process of its motion through its directly corresponding Hamiltonian operand.  While yet -- the other of such orbifold eigensets is here to work to bear a tertiary Lagrangian, in the course of the process of its motion through its directly corresponding Hamiltonian operand.  Each of these three just mentioned orbifold eigensets, is here to be traveling through a sequential series of group-related instantons, that is here to be of the same scalar magnitude of duration -- to where each of such orbifold eigensets is consequently to then to bear the same scalar magnitude of an evenly-gauged Hamiltonian eigenmetric, -- that is here to be relativistic in similtaniety, via the vantage-point of a central conipoint.  Consequently, in such a given arbitrary case -- that mass-bearing orbifold eigenset in this situation, that is here to work to bear a tertiary Lagrangian, in the process of its motion through space, -- will tend to bear the greatest Kahler-based quotient of the three; That mass-bearing orbifold eigenset in this situation, that is here to work to bear a binary Lagrangian, in the process of its motion through space, -- will tend to bear the next highest Kahler-based quotient of the three;  And Furthermore, that mass-bearing orbifold eigenset in this situation, that is here to work to bear a unitary Lagrangian, in the process of its motion through space, -- will tend to bear the lowest Kahler-based quotient of the three.   To Be Continued! Sam Roach.

Piecewise Continuous Transference of De Rham Cohomology

The more piecewise continuous that the motion of an orbifold eigenset, that is here to bear the transference of a De Rham cohomology, is to be expressed as, the more Yau-Exact that such a said orbifold eigenset, that is of a De Rham cohomology, is to tend to be translated as. This is the tendency in a Lagrangian-related manner -- because if such a cohomology is to be traced in a piecewise continuous manner, -- it will tend to only be changing in as many derivatives as the number of spatial dimensions that it is here to be moving through -- over the so-eluded-to duration, of a given arbitrary proscribed sequential series of group-related instantons.  Furthermore -- this is also the tendency in a metric-related manner, -- because if such a cohomology is to be traced in a piecewise continuous manner, -- it will then tend to maintain its tense of a dimensional-related pulsation, as well, through this so-eluded-to duration, of such a given arbitrary proscribed sequential series of group-related instantons.  I will continue with the suspense later!  To Be Continued!  Sam.

The Motion Of Mass

Isotropically stable Legendre homology works at making a Yukawa Coupling upon Calabi-Yau spaces, in so as to tug these so-eluded-to mass-bearing spaces along the multi-various mappable-tracing of space and time -- over a sequential series of group-related instantons, -- in so as to work at helping to allow for the kinematic motion of matter over the course of time.
I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.

Yukawa Versus Gliosis To Kahler-Metric

Any given arbitrary superstring that is not frayed, is always going to be Yukawa to the Kahler-Metric, yet, only when such a so-eluded-to superstring is in the process of working to attain those fractals of discrete energy that these need -- in order to both persist and exist as discrete energy -- will such superstrings actually be Gliosis to the Kahler-Metric.  The metric of a superstring of discrete energy permittivity, is its dimensional-related pulsation.  Any superstring that is not being frayed, will always work to bear a dimensional-related pulsation over time.  Yet, such an eminent tendency of a superstring to work to bear any of such a tense of a dimensional-related pulsation -- works to bear a general condition, to where, since any given arbitrary respective superstring is not literally 100 percent efficient in the "real world," discrete energy must recurrently, over time, go through a "renovation-like" process of such a prior inferred re-attaing, of those fractals of discrete energy -- to where discrete energy is to thence to be put into such a condition-related "position," to then to be able to reattain the ability to work to bear one manner or another, of a dimensional-related pulsation over time.  This process of such a said "renovation-like" activity, is when discrete energy -- after a set of iterations of the ending segments of the contingent correlative group-related instantons, in which such discrete quanta of energy are to interact directly in a Gliosis-based manner, with a respective tense of an eigenstate of the holonomic substrate of the Klein Bottle, is to happen, in order to both modulate the morphology-related qualities of the said discrete quanta of energy, and also in so as to modulate the wave-tug-related qualities of the same said discrete quanta of energy -- so that the said stringular-like phenomenology that is here to thence to be made Gliosis to the Kahler-Metric, is to both reattain its efficiency and its "stamina," over time.  Furthermore, such a said process -- works to make it easier for abelian groups to latch-on, in an indistinguishably changing manner, to the externalized shell of the multiplicit topological proximal region, -- in so as to work to help at making the functioning of cohomological attainment to be able to be possible, over time.
I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.

Space-Time-Fabric

The multiplicit wave-tug, that is applied to the mini-stringular segmentation -- that works to form the Ward-Cauchy-related field-density in the substringular -- works to form the fabric of space.  The sequential series of group-related instantons is time.  The interdependent interaction of the multiplicit wave-tug, that is applied to the mini-stringular segmentation -- that works to form the Ward-Cauchy-related field-density in the substringular, with the sequential series of group-related instantons -- is the general condition of space-time-fabric.
I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.

Noether Flow And Lagrangian-Related Path

Let us initially consider a general Stoke's-based Lagrangian-related path, that may be extrapolated in many different potential ways -- since such a said path may vary in its relative multi-dimensional depth, over time.  Let us next consider the given arbitrary respective orbifold eigenset, that is to be able to go through such a general genus of a path -- over a here considered evenly-gauged Hamiltonian eigenmetric, which may vary in its specific duration, -- when this is in consideration of the actual specific as contrasted with just the general path, that is here to be extrapolated.  Let us next consider, that the said orbifold eigenset here -- is to be undergoing a Noether-related flow, over the course of its translation through the extrapolated Lagrangian-related path -- that is here to be brought through, via an even set of a sequential series of instantons, in the process of an even-function-based Fourier series.  The higher that the tense of the Majorana-Weyl-Invariant-Mode is, that is of the said orbifold eigenset -- the more conformal invariant that the directly corresponding translation will be, of the correlative Lagrangian that is related to the transfer of the said orbifold eigenset from one spot to the next over time, that is here to be traversed over a general path that may vary in the specifics of its depth-related parameters, as is according to the specific manner of the correlative extrapolated Stoke's-related depth. The more conformal invariant that the directly corresponding translation will be, of the correlative Lagrangian that is related to the transfer of the said orbifold from one spot to the next over time, -- the more time that it will tend to take for the said orbifold eigenset to then to be able to be translated over the general said Stoke's-based Lagrangian-related path --  since the said orbifold eigenset will then tend to have less of a thrust of motion over the course of going through the said general extrapolated path, as a set of discrete quanta of energy that function to form one specific operation, to where the so-eluded-to holonomic substrate of energy as being the said orbifold eigenset, will then tend to have less energy of net transversal motion, as this will then tend to cause the general transversal Lagrangian to be impeded along its general path, when this is taken along the so-eluded-to specific path of a potentially varying depth.
I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.

Gauge-Tranformations And The Light-Cone-Gauge

Whenever electromagnetic energy scatters upon another phenomenon -- one or more photons is each (each photon), individually taken, acting in so as to strike the externalized core-field-density of the light-cone-gauge topology of another discrete quantum of energy.  So, whenever electromagnetic energy is to scatter upon anything in a Noether-related manner, over time -- the resultant Gaussian Transformation that is correlative to the Kahler-Metric, that is here in a Gliosis-related manner, may be called a gauge-transformation.  It is the Fourier-based activity of gauge-bosons -- acting in so as to "pluck" the correlative and respective second-order light-cone-gauge eigenstates, -- that works to form those Schwinger-Indices, that move in so as to flow about the Rarita Structure,  in so as to work to influence as to what genus of force is to be displayed at where, in the Ward-Cauchy realm of the substringular.  When such Schwinger-Indices come together, in so as to work to form a wave-based holonomic substrate -- that is to travel in both a transversal and in a perpendicular manner over time -- this works to form gravitational waves.  When such Schwinger-Indices work to help at localizing a multiplicit quantum of discrete energy per cohomological generation over time, -- this works to then help at forming a basis for the electromotive force.  When such Schwinger-Indices work to form a centralized knotting of eigenstates along the multiplicit Rarita Structure eigenstates -- this works to help at forming the strong force.  Furthermore, when such Schwinger-Indices work to destabilize the strong force indirectly at various loci, -- this works to help at forming the weak force.  Metaphorically think of the Rarita Structure as like the "veins" and the "arteries," in a way, in the general tense of a perception, that is over the sequential series of instantons that occur during the generally noticed duration of Ultimon Flow.  Next, -- metaphorically think of the Schwinger-Indices as the "blood" that works to help at carrying nutrients to the multiplicit array of living cells, -- by the condition that this is symbolic of the condition that the Fourier-related activity of the multiplicit Schwinger-Indices, works along the Rarita Structure, in so as to help to provide for the enactment of the basic forces that exist in nature.
 I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.

Some Additional Stuff About Cohomological Generation, I

Let us consider a discrete superstring of discrete energy permittivity, that works to move through a discrete Lagrangian path over time.  The said superstring is here to be interacting in a Gliosis-related manner, with those norm-state-projections that are in its immediate path -- in the process of moving through the Hamiltonian operand that is amidst of its said Lagrangian-related path.  Such so-stated projections, are here to be scattered upon their direct contact.  These said norm-state-projections are either to be scattered in a harmonic manner, or, in an enharmonic manner -- over the directly corresponding sequential series of group-related instantons.  A scattering at the Ward-Cauchy-related level, is said to be of a Reimman-related manner -- if the adjacent displaced eigenindices are said to have an even parity.  Furthermore -- a scattering at the Ward-Cauchy-related level, is said to be of a Rayleigh-related manner -- if the adjacent displaced eigenindices are said to have an odd parity.  If the said scattering is of a Reimman-related manner -- the directly corresponding scattering is said to be of a harmonic nature.  Yet, if the said scattering is of a Rayleigh-related manner -- the directly corresponding scattering is said to be of an enharmonic nature.  When a Ward-Cauchy-related scattering is of a Reimman-related nature -- it is said to be generating cohomology. Yet -- when a Ward-Cauchy-related scattering is of a Rayleigh-related nature -- it is said to be degenerating cohomology.  I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel Roach.

Cyclic Permutative Kahler Conditions

The more rapid that there are cyclic permutations, that are of the nature of what may here be called antiholomorphic Kahler conditions, that are here to happen to the Fourier-based activity of a Ward-Cauchy-related phenomenology -- that are to be applied to those individually taken superstrings, that work to comprise any one respective given arbitrary orbifold eigenset -- the more likely that such a said orbifold eigenset is then to work to bear a relatively higher tense of a Majorana-Weyl-Invariant-Mode, over a here ensuing sequential series of group-related instantons.
I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.

Some Stuff On Tense Of Singularity

Let us here consider a case -- in which one is to have an orbifold eigenset, that is to be traversing along a topological surface, that is of a harmonic-based sinusoidal-related nature -- over a sequential series of group-related instantons.  Let us next say that this just mentioned path that is for the so-stated orbifold eigenset, is to be of a relatively smoothly-curved or hermitian nature -- to where the curvature that is here to be being traversed, is to only to change in just as many derivatives as the number of spatial dimensions that the said orbifold eigenset is to be traveling through, over time.  One may then say that the set of singularities that are thence formed -- are then to be described of as being Lagrnagian-based hermitian singularities.  Let us next consider a case in which one is to have an orbifold eigenset, that is to be traveling along a topological surface as well, that is of a "harmonic-based" sinusoidal-related nature, over a sequential series of group-related instantons.  Let us next say that this just mentioned path, that is for the so-stated orbifold eigenset -- is to be of a relatively jagged nature -- to where the said curvature that is here to be being traversed, is to change in more derivatives than the number of spatial dimensions that the said orbifold eigenset is to be traveling through, over time.  One may then say that the set of singularities that are thence formed -- are then to be described of as being Lagrangian-based Chern-Simons singularities.
I will continue with the suspense later! To Be Continued!  Sincerely, Samuel David Roach.

Homology Versus Cohomology

Here is the basic difference between what a homology is, versus what a cohomology is:
A homology is the physical memory as to the when, the where, and the how, that either an open substringular strand or an open substringular loop has differentiated, as a Hamiltonian eigenindex, over time.  A cohomology is the physical memory as to the when, the where, and the how, that a closed substringular loop has differentiated, as a Hamiltonian eigenindex, over time.  Such physical memories may be anywhere from being at a proximal locus, that is just external to the core-field-density of the superstring -- in other words, at the Ward-Cauchy-based field that is just external to the topological stratum of the substringular eigenindex, -- to being as a physical memory that may be extrapolated from the effect of such a respective strand or a loop, that has here to have just potentially differentiated through a Lagrangian that may be mapped-out, over a Fourier Transform that involves a sequential series of instantons.
I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.

Course 20, Session 10 -- Part One

Light and all other forms of electromagnetic energy, tend to travel in multiple beams of energy, that are interconnected -- via a process known of as quantization.  Any electromagnetic energy that is here to be propagated, is to be transferred through space and time, in discrete bundles of photons, -- of which are here to be delineated upon their environment, in the form of one or more beams of energy, over the course of the general duration of time (and in the path of least time).  Different types of electromagnetic energy exist in different beam-related bundle sizes, of which work to help in causing the general condition of the many different sizes of wavelengths of electromagnetic energy -- that are here to exist as differentiating in a kinematic-related manner, over the multiplicit sequential series of group-related instantons, that are to be happening in realm of the light energy and the light matter that exist in physical space and time.  Such so-eluded-to variations in the genre of the different sizes and types of wavelengths of electromagnetic energy that are to exist in the multiverse, helps to form the individually taken operations that each specific genus of electromagnetic energy is to form -- as such electromagnetic energy is to work to influence its environment in an interdependent manner, as such said energy is to be Yukawa to other energy in the realm of space and time.  All motion exists relative to both the existence and the velocity of light, over time. Photons exist in p-fields, and photons, when individually taken, are the discrete increments of electromagnetic energy.  All light and all other forms of electromagnetic energy, exist in integer-related packets of one or more photons.  Therefore, this happens in such a manner, to where all motion exists relative to both the existence and the velocity of the general genus of the most important generic type of p-field, -- to where all motion exists relative to light.
I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.