Wednesday, July 19, 2017

Wave Modulae And Cohomological Generation

Let us initially consider the basic generic set-up, for the condition of the wave modulae of an eigenfunction.  What I am referring to is:  e^(lambda*the eigenfunction).  One may here come to grips with the three basic genre of the wave modulae of eigenfunctions, which would be:
1)  e^(lambda*the eigenfunction), when lambda is less than zero -- for degenerative cohomologies.
2)  e^(lambda*the eigenfunction), when lambda is zero -- for  purely Rham-based cohomologies.
&3) e^(lambda*the eigenfunction), when lambda is more than zero -- for  generative cohomologies.

Now, we will look at a specific example -- as to how this may be applied to a physical condition, at the sub-atomic level.:
One is to initially have a loose electron -- that is of a basically Rham-based cohomology -- to where the cohomological index is to neither work to bear a degenerative nor a generative cohomology.(lambda~0).
Next -- the said electron is to be magnetically pulled into the Ward-Cauchy-based field of an atom -- to where the cohomologies that the electron are to form are to now be of a net generative nature, to where lambda is here to be greater than 0.  (This is to then be related to what may be called a Faro wave function modulae.)
Next -- the said electron is to be struck by a photon -- to where there is the eminent formation of an antiholomorphic Kahler condition -- to where there will thus be the formation of a basically degenerative cohomological index.  In the process, as the electron is to be struck via a Calabi-Yau interaction, in the process of it going into an antiholomorphic Kahler condition, -- it is to first drop an energy level (towards the nucleus of its correlative atom), while then going back an energy level (away from the nucleus of its correlative atom) -- to where the said electron is to then to release a discrete quantum of energy, in the form of a photon, through the Fujikawa Coupling, via the Green Function.
I will explain cohomological generation later!  To Be Continued!  Sincerely, Samuel David Roach.

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