Co-linear Interdependent Spatial Translations, Related By A Factor Of "i"

 Let us initially say, that one were to have two different interdependent collinear Hamiltonian Operators, -- that are to be moving along in space.  Both of such different given arbitrary Hamiltonian Operators, are to be separated by a distance, even though both of such inferred systems of energy, are here to bear an interdependent coupling function -- via the means of some latent field, that is here to inter-bind the motion of these two different inferred sets of discrete energy. Let us next say, that their covariant spatial translations -- as these two different said given arbitrary Hamiltonian Operators are to moving along in a collinear manner, -- is to bear an interdependent difference in Yukawa Coupling, by a multiplicative factor of "i." The average motion of the two different said Hamiltonian Operators, is to work to bear a Lagrangian-related path, that is here to bear a median, that is thence to be covariant in delineation, around the midpoint of the central coni-axial of their metric-related topological structure. An example of what this may mean, in one particular given arbitrary respective case, is the following: Let us say, one of these two different said Hamiltonian Operators, is to be moving to the left in a straight line, via a unitary Lagrangian. The other of these two different said Hamiltonian Operators, however, is to be spinning relatively counter-clockwise in a smooth hermitian manner, along the center of that collinear plane, of which these two different respective Hamiltonian Operators is to be spatially translated in, -- over an equivalent span of time, via the vantage-point of a central coni-point. Since one of these two respective moving covariant structures of topological stratum, is to be moving in a linear path to the relative left, while the other of the two said respective moving covariant structures of topological stratum, is to be spinning in a relatively counter-clockwise manner, simultaneously, via the vantage-point of a  central coni-point, this may often be depicted, as being one general example of a given arbitrary type of a situation, in which such a respective given arbitrary interdependent tense of a Yukawa Coupling, that is here to exist among two different respective kinematic Hamiltonian Operators, is thence to bear a covariant relationship, that may be related by a multiplicative factor of "i." To Be Continued Later! Sincerely, Samuel David Roach.