Graph kinematics of discrete physical objects: beyond space-time. III. Heisenberg -- Dyson's two-layer physics approach

Abstract

In part III is realized the consistent development of Heisenberg--Dyson's two-layer matrix approximation to the graph formalism for postulating discrete physical objects (DPO) introduced in parts I-II in the form of discrete sets of graphs--skeleton ({\bf SvT}) or root ({\bf RvT}) $v$-trees, beyond common space--time. It is noted that already in the late-1950s one made an attempt to formulate in physical theory the discontinuity as an element of some special diagram technique. In the framework of pointed Heisenberg--Dyson's two-layer matrix scheme, with an incidence {\bf I} and a loop {\bf CD}$(δ)$ graph matrices, are got the following main results: (1) the many-``planes'' {\bf SvT} or {\bf RvT} representation of any DPO in opposition to one-``plane'' physical objects in continuous physical models; (2) the superposition of different types of interaction for any microobject where {\bf RvT} representation for short-ranged interactions (weak, strong) is one-``plane'' and for long-ranged interactions (gravitational, electromagnetic) is many-``planes''; (3) based on the incidence matrix {\bf I} (upper layer) ``graph geometry'' of real DPO describes their peculiar many-``planes'' inner structure beyond common space--time; (4) the notion of interacting ``charge'' can be extracted only from the symbolical quantities for the quasi-continuous field ``objects'' by means of the loop matrix {\bf CD}($α$) (under layer); and some other concrete results of an analysis of structural peculiarities of DPO.