In The Case Of A D-Field

A d-Field, is a substringular field -- that is here to exhibit a minimum of six spatial dimensions, plus time, -- over the course of the process of any given arbitrary directly affiliated Fourier Transformation, in which such an inferred Ward-Cauchy-related phenomenon, is here to act as being of a "d-field."  Aside from the three directly pertinent spatial dimensions that we are most familiar with, the fourth spatial dimension, is here to act as an elongated spiraling spatial dimension.  The next two spatial dimensions that are less obvious to us as people, are curled-up -- from within the Ward-Neumman confines of the four already inferred spatial dimensions, that I have here just eluded-to.  The "fifth" spatial dimension is curled-up, in such a manner -- to where it is here to be orthogonal in a Nijenhuis manner, to the fourth said spatial dimension, -- as may here be imagined in accordance to the right-hand-rule.  The "sixth" spatial dimension is curled-up, in such a manner -- to where it is here to be orthogonal in a Nijenhuis manner, to the fifth said spatial dimension, -- as may here be imagined in accordance to the right-hand-rule.  When it comes to any given arbitrary field, that is here to work to bear even more spatial dimensions than the minimum number of spatial dimensions, that may be exhibited by a d-field, -- this is what the general pattern, as to the presence of any added proximal local spatial dimensions -- that may potentially be attributed to the spatial parameters of the  Gliosis-related topological surface, of any superstring of discrete energy permittivity, -- that is here to incorporate the innate condition, of working to bear any more than six spatial dimensions plus time. Sam Roach.

Quaternionic Nature Related To Light

When an electron is to jump back-and-forth an energy level -- it is to release its spare energy, into what is to be propagated away from it as a discrete quantum of electromagnetic energy.  An electron exists as behaving as an eigenstate of a d-field -- of which is to be comprised of by a minimum of six spatial dimensions plus time.  A photon (a discrete quantum of electromagnetic energy), exists as behaving as an eigenstate of a p-field -- of which is to be comprised of by a minimum of ten spatial dimensions plus time.  The residual spare energy of an electron that is thence to be released as a photon, is as well, to happen through the Fujikawa Coupling via the Green Function.  To keep this developing concept simple, -- this addition of four spatial dimensions in the process of altering an eigenstate of a d-field into an eigenstate of a p-field, is then to work to form a quaternionic-related condition upon the Hamiltonian operation of the so-eluded-to newly formed discrete quantum of electromagnetic energy.  In turn -- this thence formed quaterionic-related condition, is then to work at tending to help the stated discrete quantum of electromagnetic energy -- when such a said quantum of electromagnetic energy is here to behave as a Hamiltonian operator, to bear the scalar amplitude that is of its directly corresponding Lagrangian-related tense of energy, to then be of such a nature in so as to bear a scalar amplitude of its directly corresponding holonomic-related tense of energy -- to then be of either the same magnitude, or, of at least of an analogous magnitude. This is, in part, what works to help at bringing to cause the innate condition -- that is of the Ward-Cauchy-related manner, in which the magnetic field of a photon that is undergoing a tense of Noether flow, is to tend to curl around the electric field of an electron -- as may be shown of as is according to the right-hand-rule.
I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.

A Little As To The Mathematics Of Cohomology

When one is to work to derive those mathematical expressions -- that are here to be utilized in so as to help at describing cohomological eigenindices and cohomological eigenstates, -- one is to initially work to derive what I term of here as being the respective given arbitrary genus of a "knotting" equation.  Such a said "knotting" equation is here to be contingent upon a Real Reimman manifold, of which is named here as "W."  If one is to try to derive a correlative Complex manifold G(c), one may take one or more Li-operators to be applied upon the said W manifold, in order to get the said G(c) manifold -- in the process of working to determine such a general condition.  In the process of working to derive such so-inferred knotting equations, one is here to be working to translate one given arbitrary Minkowski Space into a correlative given arbitrary Hilbert Space.  I can think of six general genre of knotting equations from the "top of my head."  These would be:  One for an f-field, one for a d-field, one for a p-field, one for a graviton field, one for a gravitino field, and one for a neutrino field.  This may be enough for you to digest for now.
I will continue with the suspense later!  To Be Continued!  Samuel David Roach.

Variety Of Potential Ward-Supplemental Motions For D-Field

When an orbifold eigenset that is to bear no viable Yukawa interaction with any anomalous external source -- that would work to form an unusual topological sway -- to where the initially stated orbifold eigenset is here to act as an eigenstate of a d-field, is to strike a given arbitrary surface -- in so as to result in the Ward-Supplemental translation of the just mentioned orbifold eigenset, the path that is to be taken out of the variety of paths that may potentially happen -- for the correlative motion of the said eigenstate, are based upon the set of complex roots that are to be taken out of the variety of sets of complex roots -- that the correlatively resulting Lagrangian-based Chern-Simons singularities will work to bear, for the said orbifold eigenset, that is here to act as an eigenstate of a d-field.  Such a set of complex roots that is to be determined by the potential set of the variety of sets of complex roots, tends to be, in part, to be based upon both the covariant, the codeterminable, and the codifferentiable positioning of those superstrings of discrete energy permittivity, that are here to have worked to comprise the said eigenstate, as well as the directoral-based holomorphic tendencies, that are here to be most associated with a d-field in this case.
I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.

Part Two Of Field Genus And Holomorphic Direction

In so long as there are no external anomalous forces that are here to be applied in a viable Yukawa manner to either an f-field, a d-field, or a p-field, -- an f-field will generally bear a high expectation value of working to bear its respective set of potential holomorphic directoral tendencies, a d-field will generally bear a high expectation value of working as well to bear its respective set of potential holomorphic directoral tendencies, and a p-field will generally bear a high expectation value of working as well to bear its respective set of potential holomorphic directoral tendencies.
I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.

Field Genus And Tendency Of Holomorphic Direction

Over the course of any one iteration of group-related instanton -- an f-field is an f-field, a d-field is a d-field, and a p-field is a p-field.  Yet -- over the course of any one iteration of group-related instanton -- there are often superstrings of an f-field, that may be influenced by an external source, in so as to work to bear a tendency of holomorphic topological sway, that may either be in-between the normal directoral tendency of an f-field and the normal directoral tendency of a d-field, or in-between the normal directoral tendency of an f-field and the normal directoral tendency of a p-field.  Likewise, there are often superstrings of a d-field, that may be influenced by an external source, in so as to work to bear a tendency of holomorphic topological sway, that may either be in-between the normal directoral tendency of a d-field and the normal directoral tendency of an f-field, or in-between the normal directoral tendency of a d-field and the normal directoral tendency of a p-field.  Likewise, there are often superstrings of a p-field, that may be influenced by an external source, in so as to work to bear a tendency of holomorphic topological sway that may either be in-between the normal directoral tendency of a p-field and the normal directoral tendency of an f-field, or in-between the normal directoral tendency of a p-field and the normal directoral tendency of a d-field.
I will continue with the suspense later!  To Be Continued! Sincerely, Samuel David Roach.

The Eminent Formation Of A Photon

When the Fujikawa Coupling is to  happen, at a relatively proximal local Ward-Cauchy-based region -- an electron is to release its excess discrete energy quantum, in the form of a photon.  As an ansantz, whenever the Fujikawa is to thus happen -- the eminent photon that is thus formed, is to follow a different general Lagrangian-based path, than that given arbitrary respective electron, that is here to fall back-and-forth an energy level, in so as to release a discrete quantum of kinetic energy -- in the form of a discrete quantum of electromagnetic energy.  This obvious foresight is due to the following general Ward-Cauchy-based principle:  The directly corresponding electron, is here to work to tend to bear the condition of being of a d-field.  The directly corresponding photon that is formed by the release of an excess discrete quantum of energy -- that is expelled by the earlier mentioned electron, is here to work to tend to bear the condition of being a p-field.  The d-field of an electron -- when given its general conditions of both its angular momentum and its spin-orbital momentum, -- is to bear discrete quanta of energy that work to comprise the said electron, that have one set of potential tendencies of holomorphic drive.  The p-field of a photon -- when given its general conditions of both its angular momentum and its spin-orbital momentum, --  is to bear a different set of potential tendencies of holomorphic drive, than individually taken discrete energy quanta that are of a d-field, would otherwise tend to be tugged into.  Such a general difference in holomoprhic-based tendencies, is one of the general Ward-Cauchy-based conditions, that works to help at causing the eminent photon, that is thus formed by an electron, to follow a different general Lagrangian-based path -- than the directly corresponding electron that is here to fall back-and-forth an energy level to produce such a respective photon, is here to have taken.
I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.

Dimensions Move Through

Let us consider both an f-field, a d-field, and a p-field.  Let us next say, that, over a discrete amount of time, -- both an orbifold eigenset of an f-field, an orbifold eigenset of a d-field, and an orbifold eigenset of a p-field, are to all to travel through what would otherwise be a common general Hamiltonian operand-based region.  What is here to tend to work to influence the general Ward-Caucy-based condition, in so as to help to cause both the f-field to move through a minimum of four spatial dimensions, the d-field to move through a minimum of six spatial dimensions, and the p-field to move through a minimum of ten spatial dimensions (all of these being plus the dimension of time), is that, given the general genus of the vibrations of those superstrings that are to work to make-up each of the three individually taken general genre of field-based attribute -- along with the manner by which such superstrings of such said respective given arbitrary fields are to be tugged through such a so-eluded-to Hamiltonian-based operand -- a tendency will form, in so as to have a respective minimum of four spatial dimensions (for f-fields), six spatial dimensions (for d-fields), and ten spatial dimensions (for p-fields), is to be the said case for the three different said genre of field-based attribute.
I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.

Electrons And Spatial Dimensions

Let us here, consider the motion of a given arbitrary mass-bearing superstring of discrete energy permittivity -- that is of an electron.  The individually taken mass-bearing superstrings of an electron, exist in what may be termed of as a d-field.  A d-field, over any respective given arbitrary Fourier Transformation, exists in a minimum of six spatial dimensions, plus time.  The mass-bearing superstrings of an electron tend to be Yau-Exact, to where such individually taken superstrings of discrete energy permittivity, are to here be an eigenstate of a Calabi-Yau manifold.  Over the course of any respective given arbitrary iteration of BRST, that involves the individually taken mass-bearing superstring of an electron, the drive of the angular momentum of the topological stratum of the holonomic substrate of such eigenstates of a Calabi-Yau manifold, are to here be of the general genus of the directorial-based Hamiltonian operand, -- of what amounts to as being of the mean Lagrangian path, that may be subtended from being basically right in-between the direction that is in the path in which the correlative annulus of that superstring's core-field-density is pointing in, &, the direction that the topological substrate of the external fringes of the core-field-density of the said superstring is pointing in.  This general genus of the motion of a mass-bearing superstring, along such a so-stated mean Lagrangian path, works to help at forming a harmonic tendency of a homotopic-based torsion, of which is to here help at working to help cause the respective torsional eigenindices of such a general genus of discrete energy permittivity, to tend to bear a hermitian wave-tug, that is again, of a Yau-Exact nature.
I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.