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

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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 (SvT) or root (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 I and a loop CD(δ) graph matrices, are got the following main results: (1) the many-``planes'' SvT or 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 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 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 CD(α) (under layer); and some other concrete results of an analysis of structural peculiarities of DPO.