The Ricci Flow, And The "Betti Action"

 The correlative Ricci Flow, that is here to be eminently associated with the "Betti Action," during the course of BRST Quantization, tends to be represented, as a negative Real Riemannian Number. This just mentioned tendency, works to bear the direct involvement, with the workings of a positive Betti Number. Whereas; The correlative Ricci Flow, that is here to be eminently associated with the "Betti Action," during the course of the Regge Action, tends to be represented, as a positive Imaginary Number. This just mentioned tendency, works to bear the direct involvement, with a negative Betti Number. The Betti Number, will always tend to be represented, as a Real Riemannian integer value. TO BE CONTINUED! SINCERELY, SAMUEL DAVID ROACH. 

As an aside: 

I worked to derive an equation, of which is here to relate, the Betti number of a given arbitrary specific case scenario, during a singularized iteration of BRST, and, the directly corroborative discrete energy of the Betti Action, of which is here to be directly associated, with the concurrent set of physical attributes, that are here to be eminently applicable, when the Betti number is as such. This particular equation, is:

THE DISCRETE ENERGY OF THE BETTI ACTION  

= i*e^((The Betti number)/(2*PI))/(e^(-(1/(The Betti number))).

If I properly recall mentioning the following in the past, a superstring may only be capable of compactifying/de-compactifying, by at the most 16 spatial dimensions all at once. So; By my particular model of string theory, the absolute Riemann value of the Betti number, may only be attributable, to a discrete scalar magnitude of "16." This would thereby work to signify, from what I can perceive, that when a particular "indistinguishably different" superstring is to alter, in its exhibited number of discrete spatial dimensions, by 16 of these inferred parameters all at once, that the Nijenhuis energy that is consequently emitted by the Betti Action from this, is About, 13i(Planck Transversal Energy) + (211PI*i)/(360) (Planck Radial Energy). To me; This mathematics alone, insinuates, that about 93 percent of our universe, is a combination, of what is purported to be, both dark matter and dark energy.  THANK YOU FOR YOUR SUPPORT!!!

Some More As To Schwinger-Indices And Gravity Waves

After the general Fourier-related activity of gauge-bosons -- acting in so as to "pluck" the correlative second-order light-cone-gauge eigenstates of one respective discrete quantum of energy, in a manner that is metaphorically like a harp being played -- to where this is to form Schwinger-Indices, that are thence to be propagated outward from the here directly corresponding locus of the correlative discrete quantum of energy, -- the consequent Schwinger-Indices that are thence formed, are initially formed as a fractal of what are commonly thought of as gravity waves.  Once enough of such a general genus of Schwinger-Indices are to become eigen -- via the here consequent quantization of the so-eluded-to vibrations that are here to be propagated along the proximal local Hamiltonian operand-related eigenstates that are here of the Rarita Structure -- this happens to where the consequently formed eigenstate of holonomic substrate that are to literally act, in so as to be effectual as a metrical-gauge-related eigenstate of what we would normally think of as actual gravity waves, are thence to be formed.  Since gravity waves are a set of Schwinger-Indices-related eigenindices, that come together in a quantific manner -- in so as to operate in order to perform one specific function in space and time, -- gravity waves behave as to the multiplicit vibrations along the Rarita Structure, as orbifold eigensets are to behave as those directly corresponding discrete quantum of energy that work to comprise any said given arbitrary orbifold eigenset.  Once that enough of any one specific set of Scwhinger-Indices that are formed, in so as to act as a fractal of gravity waves, are to be quantized enough, in order to perform one specific viable Ward-Cauchy-based function in time and space, -- the consequently formed gravity waves are vibrations or wave-like phenomenology, that are simultaneously propagated -- in a manner that is relatively outward and perpendicular to the proximal locus region that such individualy taken gravity waves are to be traveling through -- in the form of one relatively symmetric or one relatively assymetric homotopic gravitational-based Hamiltonian operator, that is pulled through the correlative Hamiltonian operand that it is being transferred through, as such gravity waves are to consequently to be delineated along its directly corresponding Lagrangian-based path.  Such gravity wave-based eigensets, (what are most commonly thought of as the individually taken gravity waves themselves), are extremely smaller in diameter than a wavelength of light, although such gravity wave eigensets are extremely larger than the diameter of one discrete increment of a quantum of energy.  Such gravity waves tend to have a diameter that is on the order of 10^(-18) of a meter to 10^(-21) of a meter.This would then make gravity wave eigensets, or, to keep it simple, gravity waves, -- to be basically logarithmically in-between the size of a discrete quantum of energy and the size of any respective given arbitrary wavelength of electromagnetic energy, as such a quantization of vibrations along the Rarita Structure, is made Yukawa to discrete energy--  over time.
I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David.

The Next Two Solutions To Test One Of Course 20

3)  What I mean by a "medium," is that general genus of a Hamiltonian operand, by which any respective given arbitrary electromagnetic energy is here to be traveling through such an operand, over time.  For instance, whatever the phenomenology that any respective given arbitrary electromagnetic energy is to be traveling through at the time, is thence to be of that same "medium" in which the here so-stated electromagnetic energy is to be Gliosis with, over that respective time frame in which the said "medium" is here to be correlative with such a general tense of the said energy.
4) Light scattering is that Rayleigh-based reaction of electromagnetic energy -- towards whatever the said electromagnetic energy is to strike, in so as to be re-distributed in an annharmonic manner, over time.  This involves a set of one or more photons -- to be in the kinematic process of working to strike the respective multiplicit externalized core-field-density of the light-cone-gauge eigenstate, of the discrete energy quantum or quanta that such a photon or photons are to strike, over time. Light re-quantization, on the other hand, is that Reimman-based reaction -- that electromagnetic energy is to display, of which is here to happen whenever it is to strike another set of electromagnetic energy in a Gliosis-based manner, in such a manner, in so as to work to form a harmonic re-delineation of their kinematic eigenindices, over time.  Such a Reimman-related reaction, is here to work to draw the proximal local photons towards one another -- in so as to make the resultant beam of light as both its entire whole and as the quantum of each photon that works to comprise the said beam at the same "time," just as a drop of water in the ocean is as the ocean, and as the ocean is itself, at the same time.
This is to happen, when two or more photons are to strike each other OUTSIDE from their respective light-cone-gauge eigenstates, -- yet NOT in a head-on manner, over 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.

Light Quantization

Here is one  way to look at the quantization of light in a laymen's manner -- so that it is simpler to understand.  Let us say alogorically that the smallest amount of water -- in this arbitrary example -- was a small drop of water.  When one given said drop of such water drops into a pool of water, what was initially a drop of water will here now, in a way, act as the whole pool of water in this case-- yet, the said drop of water will still act as the initial drop of water in other ways as well.  The said pool, in this case, may be thought of as a conglomeration of basically countless of such drops of water.  This may work to help explain the concept of quantization in a metaphorical manner that a layman can understand.
Likewise, when a photon quantizes into a beam of light, the said photon then acts as both the whole beam of light -- as well as acting as the individual said photon at the same time.  Here as well, the photon is the smallest amount of electromagnetic energy (here, light in this case) that still acts as the phenomenon of being electromagnetic energy.  A discrete amount of electromagnetic energy is the smallest amount of electromagnetic energy that is still electromagnetic energy.  We normally think of light when we think of electromagnetic energy. A discrete unit of electromagnetic energy is also known of as a quantum of light.  The just mentioned condition of a photon entering a beam in such a manner in so as to both act as the whole given arbitrary beam of electromagnetic energy -- as well as acting as an individual photon -- is the basic general concept as to what the quantization of electromagnetic energy is.  And, all motion is relative to the existence and the activity of electromagnetic energy -- or, to simplify, all motion is relative to the existence and the activity of light.