The following is the general idea, as to the composition of the differential geometry of a given arbitrary Fadeev-Popov-Trace eigenstate -- that is here to be of the essence of the activity of a Noether-related flow:
Initially I would like to work to begin to describe the general idea, behind such an inferred geometrical construction. Let's say that one were to consider here, that the forward-holomorphic direction is to be considered to be going towards the relative "left." Consequently -- the norm-to-forward-holomorphic direction is here to be at the relative "top," and the norm-to-reverse-holomorphic direction is here to be at the relative "bottom." One is here to have a Chi-like-shape of a component of such a Trace, that is here to have two different ellipses inscribed at the region, that is Poincare to being just external to the center of such a said Chi-like shape of a component of such a Trace, -- to where one of such ellipses, is here to act as being inter-woven upon the region, that is here to be at just "above" and to the center of the said Chi-like shape, and the other of such ellipses, is here to act as being inter-woven upon the region, that is here to be at just "below" and to the center of the said Chi-like shape. Next, for reasons that you may soon understand as to why -- let's arbitrarily take the mapping of a Laplacian-based Wilson Line, and trace this mappable line across the inferred relative "top" of this trace; as well as arbitrarily taking a mappable Laplacian-based line, and tracing this line across the inferred relative "bottom" of this trace. (These two just mentioned "lines" are not actually part of the inferred Fadeev-Popov-Trace, yet are here to act solely as a means of helping with my description of the implied Trace of such a case, as you soon shall see.) Next -- map-out a Wilson-based line, from the relative "top" mapped-out line to the relative "bottom" mapped-out line. This distance will here be of the general scalar magnitude of about 10^(-43) of a meter in length. The general Chi-like shape of a Trace, will be constructed as two intersecting trace-like curves. This Trace will here work to bear the equivalence of two intersecting curves, that are to dually be of the nature of acting on the order, as being similar to {y = x^3, y = -x^3}, except, that at the four implied corners of the overall Chi-like portion of such a Trace, the inferred appendages of the implied partial components of this said Trace, when at a level that is here to be Poincare to the topology of this inferred part of the composition of such a Fadeev-Popov-Trace eigenstate, is here to mildly change in its concavity in a Nijenhuis-related manner, over a relatively brief translation of space, in so as to work to complete the Chi-like component of such an eluded-to individually taken eigenstate. Next -- the two earlier mentioned oval-like shapes, that are here to be inscribed at those relative positionings, that are here to be inter-woven at both just above and just below the intersecting center of those curvatures, that are here to be of the earlier inferred Chi-like partial component of the general genus of such a Trace, whose differential geometry I am working to describe, are here, to work to bear a scalar magnitude, of a maximum "length," that is here to be on the order of about 5*10^(-44) of a meter in spatial translation; as well working to bear a scalar magnitude, of a maximum "width," that is here to be on the order of about 2.5*10(-44) of a meter in spatial translation. Both of such inferred "oval-like-shapes," are here to reach their respective norm-to-forward-holomorphic end, and, their respective norm-to-reverse-holomorphic end, -- at the general proximal local region, at which one had here to have mapped-out the respective Laplacian-related Wilson Lines at those implied extremes, that I had earlier indicated, in so as to get a better idea as to the gist of what I am working to convey here.
I will continue with the suspense later! To Be Continued! Sincerely, Samuel David Roach.
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