Monday, February 1, 2016

Euclidean Expansion Versus Clifford Expansion

Let us initially take into consideration, a set of five orbifold eigensets -- that are initially localized in a proximal-based general region that is in the substringular.  Let us next consider the Ward-Caucy-based condition of all five of such orbifold eigensets -- as initially existing in a tense of Majorana-Weyl-Invariance, at a relatively set general locus -- over a duration that would here involve a relatively transient sequential series of group-related instantons.  Let us next consider the given arbitrary condition of such a case -- to where the said set of eigensets will have here worked to bear the Laplacian-based condition of having one central orbifold eigenset, that was to here be surrounded by the other four of such so-eluded-to orbifold eigensets, as may be extrapolated here in the said relatively transient sequential series of group-related instantons.  Let us say that a group-attractor were to act upon the so-stated set of external-based orbifold eigensets of this respective given arbitrary case -- in so as to cause the four said orbifold eigensets that were said to initially surround the so-stated central orbifold eigenset, to be then perturbated from being adjacent to the said central orbifold eigenset of such eigensets, -- in such a manner in so as to cause the so-stated surrounding orbifold eigensets to diverge in a covariant-based manner, away from the central said orbifold eigenset, over a relatively transient duration of time.  Let us next consider, that the Hamiltonian-affiliated Lagrangian-based path of the four so-stated diverging orbifold eigensets, were to each, when this is individually taken, be translated along the so-eluded-to Hamiltonian operand -- in which these said eigensets are to here be moving through, to where this will be of a mappable tracing -- that is here to be translated as a unitary gauge-metrical Hamiltonian-based operation, that is to here be differentiating in a Fourier-based manner, over time.  One could then say that the expansion of the scalar magnitude of the region that would then exist, that is of the then diminishing scalar amplitude of the field that may here be extrapolated by the respective given arbitrary ever weakening coniaxial, that had initially worked to join the five said orbifold eigensets, that could be traced among the interdependent field that would here work to interconnect the interactions that would then exist among the eigenindices that would act in so as to work to form the five so-stated orbifold eigensets, would be an expansion that could be considered as increasing in its scalar magnitude in a euclidean-based manner over time.  Soon -- a similar example, yet, instead, as a description of a Clifford Expansion.  I will continue with the suspense later!
To Be Continued!  Sincerely, Sam Roach.

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