Casimir Invariance And The Kahler Manifold

 When a Casimir Invariant field is to be physically applied, upon the topological manifold of a Kahler Manifold, in a Gliosis-Based manner, at a level that is Poincare to the externalized core-field-density, of the particular Hamiltonian Operator, that is here to be expressing such an inferred Kahler-Related field, the morphological contortion that is here to be viably effectual, upon the Riemann surface of the directly corroboratively inferred Gaussian-Based cohomological stratum, may often tend to work as behaving in a hermitian manner, as being somewhat analogous to the general processes, that may be insinuated, when in retrospect to the reductional kinematic operation of the Fujikawa Coupling, as via the Green Function. SAMUEL ROACH.

Analogy To The Fujikawa Coupling

 The smoothly hermitian folding of a flat cohomology-related world-sheet into a rounded cohomology-related world-sheet, is relatively analogous to the Fujikawa Coupling. SAMUEL ROACH.(1989).

Light Into Kinetic Energy

 When a given arbitrary superstring, of a discrete quantum of electromagnetic energy permittivity, as exemplified  by the particle-related nature, of the holonomic permittivity of a photon, is to spontaneously convert into a superstring of discrete kinetic energy permittivity, — this general process, acts as the Inverse Operation, of the Fujikawa Coupling via the Green Function. Sincerely, SAM ROACH. (1989).

Release Of Relative Yukawa Bearing

When the general Ward-Cauchy-related process is here to be going on, during which the residual kinetic energy of an electron is to be released in the form of a photon -- there is here to be one directly corresponding open-looped superstring of discrete energy permittivity, that is then to release the immediately prior state that it had had, when in terms of its relative Yukawa bearing upon the correlative respective electron, to where right after such a said general process is to occur -- the here just released correlative discrete quantum of a Legendre homology, is then to undergo the general process,  that is here to be directly involved with the activity of the Fujikawa Coupling,  which is here to happen via the manner of activity that is known of as being of the Green Function, -- in so as to ensue as to work to form one given arbitrary respective discrete quantum of electromagnetic energy.
I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.

As To Electromagnetic Energy And Cohomological Generation

Let us initially consider a photon that is colliding with an electron, that is of one given arbitrary atom.  The said electron is situated here at the relative external energy level or valence shell of the directly corresponding atom, that is here being discussed.  As the so-mentioned photon is here in the process of scattering upon the correlative electron -- the photon is here to temporarily become entropic, while the electron that is here to be collided into in a Gliosis-based manner, is to consequently jump back-and-forth an energy level, -- in so as to then to undergo the Fujikawa Coupling, to where the said electron is to result in working to release its spare discrete kinetic energy in the form of a photon (in the form of a discrete quantum of electromagnetic energy).  The earlier mentioned photon, that had just scattered upon the so-stated electron, in so as to become entropic -- is then to degenerate cohomology -- in the process of rebounding from an initial Rayleigh-related scattering, back into subsequently re-quantizing into the Hamiltonian operand of the respective general beam of electromagnetic energy -- that is proximal local to the so-eluded-to electromagnetic permeation of the Ward-Cauchy-related region, in which the electromagnetic energy is here to be scattering within.  During the course of the same general evenly-gauged Hamiltonian eigenmetric, the process of the Fujikawa Coupling, -- in which the electron that was just struck at the externalized core-field-density of its correlative light-cone-gauge eigenstate, is so as to release its residual spare discrete kinetic energy into a photon, -- is to work to generate cohomology.  Consequently, the scattering of light works to both degenerate cohomology in one genus of manner, while also working to generate cohomology in a different genus of manner -- as the correlative discrete quanta of electromagnetic energy is sprung upon the holonomic substrate of a mass-bearing discrete quanta of energy, in a Gliosis-based manner over time.  This is here to be a balance, that is here to be formed between that general Hamiltonian operation of entropy, that works to degenerate both cohomological eigenstates and cohomological eigenindices, -- and that general Hamiltonian operation of electromagnetic induction, that works to generate both cohomological eigenstates and cohomological eigenindices, over time.
I will continue with the suspense later!  To Be Continued! Sincerely, Samuel David Roach.

Part Two As To Why Gauge-Transformations Are Thus Called

When a superstring of discrete kinetic energy permittivity from an electron is to undergo the Fujikawa Coupling via the Green Function, in the process of being expelled from the said electron into the form of a photon, -- the correlative open string of discrete kinetic energy permittivity is to then to be transformed into a closed string of discrete electromagnetic energy permittivity over, the course of the so-eluded-to duration of such a correlative Fourier Transformation.  An open string is fermionic.  A closed string is bosonic.  Fermionic superstrings of discrete energy permittivity work to each bear five second-order light-cone-gauge eigenstates to work to comprise the one first-order light-cone-gauge eigenstate, that is to directly correspond to that respective given arbitrary fermionic superstring.  Bosonic superstrings of discrete energy permittivity work to each bear ten second-order light-cone-gauge eigenstates, to work to comprise the one first-order light-cone-gauge eigenstate that is to directly correspond to that respective given arbitrary bosonic superstring.  When the Fujikawa Coupling is to happen to one given arbitrary respective fermionic superstring as such, each of the five second-order light-cone-gauge eigenstates that had here to have worked to form primarily the wave-based quantum of the discrete energy impedance of the directly corroborative discrete quantum of energy bundle (via the net overall Schwinger-Index eigenstate that is to thus to be formed by those vibrations, that are here to be made by the "plucking" of the individually taken said second-order light-cone-gauge eigenstates), -- is to retie into ten second-order light-cone-gauge eigenstates, that are then to be of the discrete energy quantum bundle of the here resultant bosonic superstring as such.  The second-order light-cone-gauge eigenstates that are of a bosonic superstring of discrete energy permittivity, always tend to bear half of the cross-sectional thickness of the second-order light-cone-gauge eigenstates that are of a fermionic superstring of discrete energy permittivty.
I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.

Part Two Of Session 7 Of Course 20

The first type of such scattering that I will introduce you to in this part of the course, is that general genus of scattering -- that is to occur, when a beam of light or a beam of any other form of electromagnetic energy, is to strike another phenomenon, - that is, for all practical purposes, a shear form of matter or mass, that is here to be positioned in the immediate Lagrangian-based path of the said electromagnetic energy, as an eigenbase of a respective Hamiltonian operand, to where the so-eluded-to mass-bearing superstrings of discrete energy permittivity, are to be in the path of that electromagnetic energy that is here about to strike it -- when one is to consider that electromagnetic energy is to travel in the direction of least time.  This is to  happen, when that electromagnetic energy that is about to strike the so-eluded-to mass-bearing manifold -- is to bear a cohomological mappable-tracing, that is to have a directoral-based bearing that is directed in a geometric manner, -- towards the Ward-Cauchy-based locus of a set of one or more orbifold eigensets of mass, -- to where the so-eluded-to propagation of a beam that is to here to act as a Calabi-Calabi-related manifold, is to be directed upon the topological stratum of a Calabi-Yau-related manifold.  Electromagnetic energy is propagated from a given source.  An electromagnetic beam of energy is to be propagated through a vacuum, at a tending velocity of 3.0*10^8 meters per second.  As a beam of electromagnetic energy is to strike another orbifold eigenset, that is comprised of by the holonomic substrate of mass-bearing superstrings of discrete energy permittivity, -- the photons are to collide here in an individually taken manner, upon the externalized core-field-density of the light-cone-gauge-related eigenstate that is most is its path, as an eigenstate that is to be propagated in the direction of least time, -- to where the resultant collision of each resulting scattered photon upon the said externalized field-density of each directly corresponding discrete quantum of energy, is to consequently act in so as to work to cause a back-and-forth motion of each core electron that is to have just been struck in an eminently Yukawa-based manner, to where this motion is to then to tend to result in the release of the excess energy of each electron that had just been struck, in the form of each individually taken photon.   This is the general tendency, when light is to strike mass-bearing manifolds -- since electrons orbit the outer part of an atom, and mass tends to exist in atoms.  It is the E(8)XE(8) strings that act, in so as to hold together the multidimensional structure of a sub-atomic particle -- like a metaphorical "microtubule," that works to help to allow for the resultant Gliosis-based collision, that is of the tendency of a photon that is to strike an orbifold eigenset of an electron -- to domino-out such an inward thrust, in so as to then to push the multiplicit electron into the means of such a so-eluded-to Fujikawa Coupling.
I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.

Last Test Solutions To The First Test Of Course 20

5)  Light that is to be in the process of traveling through any medium other than a vacuum, will tend to be slowed-down via the so-eluded-to process of going through such an inferred medium.  What happens in general, as light is to be going through a medium that is to slow its velocity -- is, that the said light is initially scattered by the topological stratum of such a general genus of phenomenology, to where the just scattered photons are to then go from an annharmonic re-delineaton to then such said photons are to then to be brought back into a proximal local orbifold eigenset of electromagnetic energy -- to where, until such so-eluded-to photons are to be re-scattered, such photons are to then to move in the direction of least time, until these are to be re-scattered, until these discrete quanta of electromagnetic energy are to again to be annharmonic in re-delineation until these are to be brought back into a proximal local orbifold eigenset of electromagnetic energy, to then such photons are to then to again to travel in a relatively straight manner in the direction of least time, and so on -- as is as according to the processes of Snell's Law.

6)  The Green Function, as it is to here to be applied to the processes of the Fujikawa Coupling, is a mathematical means of working to determine as to how the multiplicit discrete quantum of kinetic energy, that is to be released by an electron that is to here to drop back-and-forth an energy level -- is to bend in a hermitian manner, in so as to work to form a resultant consequent bosonic string that is known of as a photon.  (This "Green Function" works to describe how a discrete quantum of electromagnetic energy, is to be formed by the hermitian bending of an open strand of substringular topological stratum -- into that closed loop phenomenology as to then to work to become a photon. Such a hermitian bending is to here to be consistent in only to change in as many derivatives here, as the number of spatial dimensions that it is to be traveling through, over the directly corresponding successive series of instantons in which such a change is to be occurring in.)

7)  A two-dimensional string of a photon, is to move through a minimum of 10 spatial dimensions plus time -- as it is to be traveling via any consequent Fourier Transformation.  The additive spatial dimensions are to be traveled through -- in-between BRST and the end of any directly associated iteration of instanton.  Such a so-eluded-to string, during BRST, is to have a circumference that is equal to the Planck-Length divided by a factor of 3*10^8.  During the ensuing Regge Action, such a superstring is to "stretch back out" to having a circumference that is equal in scalar amplitude to the Planck Length.  Whereas, a gauge-boson is a closed-loop, that is of a higher spatial dimensionality during BRST (but of a lower spatial dimensionality during the ensuing Regge Action) -- that is to "pluck" light-cone-gauge eigenstates like a harp -- in so as to work to form Schwinger-Indices that may be thought of as gravity waves.  Such a genus of a closed-loop phenomenology that is of the nature of being a gauge-boson -- is to bear a circumference of twice the Planck Length.
I will continue with the suspense later!  To Be Continued! Sincerely, Samuel David Roach.

First Two Test Solutions -- Test One Of Course 20

1)  The Fujikawa Coupling is a Ward-Caucy-based inter-relationhip, that is of the nature of that general genus of activity that is to happen in the substringular, when the two correlative ends of the open-loop phenomenological stratum of one discrete quantum of the kinetic energy permittivity of an electron -- that is in the process of being released from that said electron -- are to be brought together in a hermitian manner, via two covariant zero-state norm-state-projections, in such a manner in so as to help at working to form what is here to be the resulting holonomic substrate of one discrete photon.

2)  In any medium other than a vacuum, in which the light that is here to be traveling through such a medium, is here to be moving through the processes of Noether Flow over time, -- to where the said light is to go from initially scattering upon the holonomic substrate-based phenomenology of such a medium, while then going into a manner of then re-quantizing with other electromagnetic energy that is proximal local to the direction of the propagated motion of the said light, while then traveling in a relatively optimum-related "straight" manner until it is scattered again, and so-on, -- to where this is to happen in such a manner in so as to bend as little as feasible as is according to Snell's Law -- as it is to travel through "the direction of least time."

I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.

Session 6 Of Course 20, Test Questions To Test One

1)  Describe the Fujikawa Coupling.

2)  Describe the bending of light in a medium.

3)  What do I mean by a medium?

4)  What is the difference between light scattering and light re-quantazation?

5)  Discribe how light slows down in a medium.

6) Describe the Green Function in terms of the Fujikawa Coupling.

7)  What is the difference between a 2-dimensional superstring of discrete energy permittivity that is correlative to a photon, and the closed-loop phenomenology of a gauge-boson?

I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.

As To Dissipated Kinetic Energy

Kinetic energy that is dissipated, tends to be converted into one of the following "things," as long as it is not frayed.:  This said kinetic energy tends to either be converted into:  Electromagnetic energy, via the Fujikawa Coupling, as is according to the Green Function;  or, it is converted into a mass-bearing superstring of discrete energy permittivity; or, it will make an indistinguishabley different perturbation in its reference frame of Hamiltonian operation; or else it will tend to be recycled in its Ward-Caucy-based conditions, into a certain Hodge-based holonomic substrate -- that is of a given arbitrary scalar amplitude of norm-state-projection(s).  I will continue with the suspense later! To Be Continued!  Sincerely, Sam Roach.

Chan-Patton Rules And Parity

The Chan-Patton conditions, that are appertaining to the Ward-Caucy relationships of the electrostatics of any respective given arbitrary atom -- that are to here appertain to the parity of an electron, will tend to work to force the correlative one-dimensional superstring and its directly corresponding counterstring -- to bend into a resultant two-dimensional superstring and its correlative two-dimensional counterstring, in a hermitian manner.  This will then work to tend to cause the said string and its counterstring, to thereby bend via the Fujikawa Coupling -- as is to here be in accordance with the Green Function.  The Chan-Patton conditions of parity, are here to be the case for the smooth energy relationships -- that exist for any discrete quanta of kinetic energy permittivity, that is to ensue as being released by an electron, when it works to drop back-and-forth an energy level.
I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.

A Little Reminder -- The Fujikawa Coupling

Electrons may be viewed of as mass that is energy that is wave that is particle, at the same time.  When an electron drops an energy level, while then returning to its immediately prior energy level -- a discrete amount of energy is then to be released from the said electron, in the form of a photon.  A photon is a discrete quantum of electromagnetic energy.  This happens, by the process of the directly corresponding one-dimensional superstring and its counterstring, that is released by the electron of such a case -- when it is tugged into bending in a hermitian manner -- to then be formed into a respective bosonic superstring and its correlative counterstring of discrete energy permittivity, -- via the Fujikawa Coupling, over a successive series of instantons.  The so-stated bosonic superstring of such a respective given arbitrary case, is more associated with the particle nature of a discrete quantum of electromagnetic energy permittivity -- while the so-stated correlative bosonic counterstring of such a case, is more associated with the wave nature of a discrete quantum of electromagnetic energy permittvity.  In the meanwhile, the respective light-cone-gauge eigenstate -- that is correlative to this given case, is altered from working to bear ten second-ordered light-cone-gauge eigenstates, to then working to bear only five second-ordered light-cone-gauge eigenstates ( as such said eigenstates are to then double-up in the Hodge-Index of the mini-stringular segmentation of their holonomic substrate, as to the cross-sectional thickness of the correlative chord-based topology of the so-eluded-to substrate, that is of the pheonomenology of such second-ordered eigenstates).  The correlative Fadeev-Popov-Trace eigenstate, is to here be torqued by this overall process -- yet, it will tend to still bear basically the same general genus of its morphological topological substrate, over the course of the process of the so-eluded-to group-metric of the Fujikawa Coupling.
I will continue with the suspense later!  To Be Continued!  Sincerely, Sam Roach.

Part Four Of Session 2 Of Course 20 -- Calabi Manifolds And Calabi Interactions

Do you remember me mentioning the two sets of zero-norm-state-projections that work upon that discrete quantum of kinetic energy permittivity, in order to allow for that process that may be called the Fujikawa Coupling via the Green Function?  This involves one of such sets of zero-norm-state-projections, that is to here act upon the pointal-based quantum of discrete kinetic energy permittivity (the respective given arbitrary superstring) -- and one of such sets of zero-norm-state-projections, that is to here act upon the wave-based quantum of discrete kinetic energy permittivity (the correlative respective given arbitrary counterstring).  The angle that exists in-between the locus of Gliosis-based contact, in which the initially so-stated set of zero-norm-stated projections is to be working to form an abelian-related Fourier-based Yukawa Coupling upon the said superstring of discrete pointal-based kinetic energy permittivity, in so as to undergo a successive set of iterations of group-related instantons, in so as to work to allow for the correlative activity of the Fujikawa Coupling via the Green Function -- in so as to help the said discrete quantum of kinetic energy permittivty to subsequently work to form a photon -- and the Laplacian-based position-based iterative delineation at which the correlative respective Fadeev-Popov-Trace eigenstate is to here be in the process of being "tagged-along," is of a Ward-Caucy-based inter-relation of 22.5 degrees. As well, the angle that exists in-between the locus of Gliosis-based contact, in which the secondly so-stated set of zero-norm-state-projections is to be working to form an abelian-related Fourier-based Yukawa Coupling upon the said counterstring of discrete wave-based kinetic energy permittivity, in so as to undergo a successive set of iterations of group-related instantons in so as to work to allow for the correlative activity of the Fujikawa Coupling via the Green Function -- in so as to help the said discrete quantum of kinetic energy permittivity to subsequently work to form the counterstring of a photon -- and the Laplacian-related position-based iterative delineations at which the correlative respective superstring that is of the pointal-based nature of discrete kinetic energy permittivity, is to to here be in the process of being "tagged-along," is of a Ward-Caucy-based inter-relation of 22.5 degrees.  Due to the trivially isomorphic assymetry that is to here exist, in both of these two said general cases, of a proximal localized Ward-Caucy-based torsioning, that -- due to the just mentioned manner of assymetry -- works to form an abelian eigenbase of a general Fourier-related activity, in spite of the non-abelian nature of the Laplacian-related delineation of such a respective torsioning.  In both the case of the superstring, and in the case of the counterstring -- the correlative individually taken set of zero-norm-state-projections, will then work to form the equivalence of a supplemental-based wave-tug upon the Gliosis-based locus as to where the so-eluded-to discrete quantum of kinetic energy permittivity is to bear its so-eluded-to Yukawa Coupling, as to the ensuing activity of what is here to be the activity of the said Fujikawa Coupling, to where, in spite of the so-stated angling of the Laplacian-based Hamiltonian curvature that is to here be pushed at an angle that is not actually supplemental, -- the resultant Hamiltonian-based operation of the wave-tug that is to be applied in both of the eluded-to cases of a Yukawa-based thrust -- will then work to form a propagation that is to here happen to both the superstring and to its counterstring simultaneously via the vantage-point of a central conipoint, that is of a relative Wilson linearity to, what would be in both cases, in the relative forward-holomorphic direction as to the directoral tug of the then forming photon and its correlative counterstring.  I will continue with the suspense later! To Be Continued! Sincerely, Sam Roach.

The Second Part Of Session 2 Of Course 20

As the substringular process that is appertaining to that operation by which a set of two correlative zero-norm-state-projections, will here work to help to cause one respective given arbitrary superstring to undergo the Fujikawa Coupling via the Green Function -- in so as to work to assist one given arbitrary maximum contracted discrete quantum of kinetic energy, that is released from the Ward-Caucy-based bounds of an electron, to form one given arbitrary respective discrete quantum of electromagnetic energy -- there is here to be as well, at a proximal localized Fourier-based gauging, another set of two correlative zero-norm-state-projections, that will work here to help to cause the directly corresponding counterstring, that is correlative to the said superstring, to work to form the counterpart-based Fourier-based activity of the Fujikawa Coupling via the Green Function.  This happens, in so as to work to help to allow, for not only the particle-based nature of the here proximal localized quantum of discrete energy permittivity to be able to then form a photon, but as well -- to work to help to allow for the wave-based nature of the here proximal localized quantum of discrete energy permittivity -- to then be able to form a photon.
I will continue with the suspense later!  To Be Continued! Sincerely, Samuel David Roach.

Part One Of Session 2 Of Course 20 -- Calabi Manifolds And Calabi Interactions

The Fujikawa Coupling is central, not only to that activity that is related to the formation of two-dimensional superstrings of discrete eletromagnetic energy permittivity -- that are known of as photons -- From the Fourier-based activity of one-dimensional superstrings of discrete kinetic energy permittivity, that has to have here just dropped an energy level from within the Ward-Caucy bounds of a respective given arbitrary atom -- yet, it is also quintessential to the Fourier-based translation of having to work to help in the process of causing one respective individually taken fully Lorentz-Four-Contracted one-dimensional open-strand of plain kinetic energy permittivity, to be able to thenceforth work to help in the formation of a fully contracted closed-loop two-dimensional superstring that is of a discrete bosonic-based nature.  The Fujikawa Coupling is what had initially worked to form the light-like energy, from those initial open-strands of individually taken eigenstates that were of the correlative disturbances of space, that had been just struck by whatever worked to form the Big-Bang -- by the resultant of that discombobulation that had happened right after the core of the Big-Bang was struck, in so as to work to form the initial energy that had subsequently worked to form the multiverse, this of which had to have happened -- soon after the initial Higgs Boson eigenstate or the Isoelliptiabelianoid, had worked to form the initial set of superstrings of discrete energy permittivity.
I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.

Part 6 Of Session One Of Course 20 -- Calabi Manifolds And Calabi Interactions

When an electron drops back-and-forth in energy levels -- this general genus of activity, works to form an antiholomorphic Kahler condition.  This is on account of the condition, that such a said electron is to here immediately reverse in the general relative holomorphic direction -- as it works to drop an energy level.  Such a so-stated antiholomorphic Kahler condition, works to then cause the ensuing activity of a proximal localized Kahler-Metric.  This will then tend to work at helping to cause the emission -- of what is to then exist from within the Ward-Caucy bounds of the here directly pertinent electron, as the spare energy that is to here be brought into and then out of the so-stated electron, on account of the initial quantum leap back-and-forth of the said electron, to and fro the respective given arbitrary energy levels. The here ensuing activity of the so-eluded-to eigenstate of the proximal localized Kahler-Metric, will then work to help at bringing in the local Yukawa-based interaction -- of those two individually taken zero-norm-state-projections, that will then act, in so as to help in the process of the ensuing eigenstate of the respective correlative Fujikawa Coupling via the Green Function, in so as to help in the process of working to form a photon.
I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.

Part Five Of Session 1 Of Course 20 -- Calabi Manifolds and Calabi Interactions

As one one-dimensional superstring of discrete energy permittivity is being released from the Ward-Caucy bounds, of any respective one directly corresponding electron -- the local centralized knotting of the Rarita Structure eigenstate, that is most directly affiliated with the locally associated Fourier-based differentiation, that is of the said respective electron -- is relatively discombobulated from its immediately prior condition.  The thence caused decrease in the need, as to the amount of kinetic energy that the correlative electron is to then have, is to then result in the just previously stated relative discombobulation.  Such a so-eluded-to back-and-forth wave-tug, that is applied to the Ward-Caucy-based conditions of the here pertinent electron, happens -- as it is to be tugged from initially  moving inward into then immediately moving outward -- of which works to help in causing the tendency of such a released discrete quantum of energy, to then be pushed into that directoral-based holomorphicity, that is in the opposite relative direction from that by which the correlative nucleus of the directly pertinent atom is in.  Such a drop, in and of itself -- in the corresponding energy level of the directly corresponding electron, will then act at such a rate --  by which the specific one-dimensional strand of energy, that is to here be released, will then tend to be brought to the "outskirts" of the Ward-Caucy bounds of the correlative electron, as a fully contracted open strand of kinetic spacial disturbance.  As the said open strand of fully contracted kinetic energy, is to then be in the process of being pushed-out of the correlative electron, the two individually taken zero-norm-state -projections that both work -- in so as to tie the two ends of the initially stated one-dimensional superstring together, in so as to work to form a photon from the now released kinetic energy -- this of which has here been emitted from the so-stated electron, to where the process itself of the Fujikawa Coupling via the mathematical conditions that may be eluded-to by the Green Function, work to help in so as to provide that needed additional thrust, to the said emitted discrete quantum of kinetic energy, -- in so to then work to cause the then formed photon, of which is one discrete quantum of electromagnetic energy, to result in going at the speed of light -- when this is taken in multi-consideration with the directly associated Ward-Caucy-based conditions, that are to here be correlative to the locally proximal state, that may be associated with Snell's Law.
I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.

Part Four Of Session 1 Of Course 20 -- Calabi Manifolds And Calabi Interactions

Bosonic superstrings of discrete energy permittivity, work to bear a circumference that is equal in a Laplacian-based manner -- to a scalar amplitude that is of the equivalence to the Planck Length.  For instance, the Laplacian-based length of any respective given arbitrary one-dimensional superstring of discrete energy permittivity, is of the scalar amplitude of one Planck Length.  Whereas, the Laplacian-based circumference of any respective given arbitrary two-dimensional superstring of discrete energy permittivity, is of the same Sterling approximation of scalar amplitude of one Planck Length.   Photons have a circumstance, that is equivalent in scalar amplitude -- to the length of a fully contracted one-dimensional superstring of discrete energy permittivity.  For instance, when any given arbitrary respective one-dimensional superstring of discrete energy permittivity -- that is of the directly corresponding circumstance of a discrete quantum of energy, that is released as the spare energy that is emitted from a photon that has jut dropped an energy level -- has just worked to leave the Ward-Caucy bounds of the physical bounds of the said respective electron, the so-stated one-dimensional superstring works to undergo what may be termed of as the Fujikawa Coupling, via the correlative math that may be extrapolated as what is termed of as the Green Function.  What this entails in general, is that the so-eluded-to open strand of discrete energy permittivity, is to here be propagated from the general Ward-Caucy bounds of the electron, in such a manner to where the directly corresponding end-points of what was the initially considered as of the said one-dinensional string, are to then be pulled together in a hermitian-based manner, -- to where these said endpoints are to here be drawn together In the relative holomorphic direction At the relative reverse-holomorphic side of such a so-eluded-to substringular projection of Hamiltonian-based motion, by which these ends are to then come together, in so as to work to form what is to then become the holonomic substrate of one discrete photon.  It is the holonomic substrate of two covariant, codeterminable, codifferentiable respective given arbitrary zero-norm-state-projections, that are to here act upon both respective individually taken ends of the so-stated initially mentioned one-dimensional superstring of discrete energy permittiivty, that act in so as to work to push these said end points into each other--  in so as to work to form a closed loop from the so-eluded-to initially inferred open-loop, in so as to work to form one discrete quantum of electromagnetic energy permittivity.
I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.

The Noether Current And The Ante-De-Sitter/De-Sitter Mode

The inter-relationship of a mass-bearing superstring, to the Ante-De-Siter/De-Sitter tense of the centralized knotting of an eigenstate of the Rarita Structure -- when such an inter-relationship is unloosed, from the pretense of the bosonic nature of a mass-bearing string to the pretense of a fermionic string of plain kinetic energy -- is analogous but different from an inverse relation of the Green Function via the Fujikawa Coupling.  A bosonic mass-bearing string may be inverted into the square of the directly pertinent centralized knotting of the correlative Rarita Structure eigenbase -- as it is unlooped into a set of fermionic strings of plain kinetic energy.  For every eigenstate of the Ante-De-Sitter/De-Sitter effect, that is viable in a given arbitrary respective locally proximal substringular region -- that is Yukawa upon an eigenstate of a Calabi-Yau-based index that exists in the substringular, there is the tendency of there being a potential of up to a total of 9*10^16 times as many open-loop-based energy quanta that are rippled through the directly corresponding Rarita Structure eigenstate, of this given respective case scenario.