Non Abelian/Abelian Vector Bundle

 Let us, at first, consider the holonomic substrate of a given arbitrary cohesive set of discrete energy quanta, -- to act as being the overall energy, of a given arbitrary respective Ward-Cauchy-related system. This implied overall energy of a system, is often referred to as being called, the Hamiltonian Operator. The general physical attribute, of the group action-related behavior of a holonomic entity, may be thought of as being the general characteristic of isotropism. In this particular case scenario; let us minimize the focus upon the potentially proximal local presence, of any invariably latent Nijenhuis tensors. Let us next think of the general case scenario, in which the just mentioned Hamiltonian Operator, (in which the earlier stated cohesive set of discrete energy quanta, is here to act as the overall energy of the respective system), is to potentially directly interact, at the Poincare level, with the topological surface, of an ulterior Ward-Cauchy-related manifold, -- to where one may consequently say, that the said respective cohesive set of discrete energy quanta, that is here to be of the initially inferred general case at stake, is then to work to bear a potentially Gliosis contact, with the earlier inferred topological  manifold, that is here to act as the general type of a phenomenology, that is here to be potentially struck in a covariant manner, by the eminent impact of the motion of the said respective cohesive set of discrete energy quanta -- that I had initially brought-up in this discussion. Let us next call the direction-related tense of the holonomic entity, that is of the initially inferred set of energy quanta, to act as the Hamiltonian manner, of a kinematically delineated vector bundle. If the potentially impending direct contact of the Hamiltonian-related vector bundle, as interacting with the topological surface of that manifold, which is here to be potentially eminently struck, were to more than likely spontaneously work to bear the relative proximal local presence, of a tense of isotropic "slippage," then, one may consequetnly say, that the general characteristic of the reductional tense, of such an implied genus of a holonomic vector bundle, is then to be of the respective reductional nature, of acting as a Hamiltonian-related non abelian vector bundle. However; if the potentially impending direct contact of the Hamiltonian-related vector bundle, as with the topological surface of that manifold, which is here to be potentially eminently struck, were to more than likely spontaneously work to bear a relative lack of isotropic "slippage," then, one may consequently say, that the general characteristic of the reductional tense, of such an implied genus of a holonomic vector bundle, is then to be of the respective reductional nature, of acting as a Hamiltonian-related abelian vector bundle.  To Be Continued, As "Advertised"  -- "At A Computer Near You!" SAM.