Discrete operator fields as carriers of causal spacetime structure. Internal symmetry

An attempt is made to set up a model of spacetime in the form of a discrete, causally ordered set of local elements – uniform sets of field operators. An algebraic description of the causal connection between two such elements that are nearest neighbors in accordance with the ordering is constructed by means of a specially formulated principle of correspondence with Lagrangian gauge theory. A necessary condition for the possibility of the construction is the requirement that the internal symmetry group be $SU(20)$, the spin $1/2$ fermions form a multiplet of dimension (190), and the spinless bosons a multiplet of dimension (35700). The possibility of interpreting the proposed special class of solutions of the constructed equation as a discrete spacetime net is discussed.