Symmetry in Nonlinear Mathematical Physics - 2009

George Stavraki (Dorodnicyn Computing Centre of the Russian Academy of Sciences, Moscow, Russia)

Quantum model of geometrical extension

Based on the idea about the identity of space-time and physical vacuum the necessity of the refusal from numerical model of geometrical extension is postulated. The new description is constructed with the help of the correspondence principle with operator field theory. Instead of a world point a universal supermatrix complex U is supposed to be the carrier of virtual local events. This complex combines total set of Heisenberg local fields operators together with their spin-group basises in the Fermi-fields representation. The fundamental element of the extension is described in the model by the equation of the noncommutative algebra, closed on two complexes U(1), U(2), connected by one vertex of virtual fields interaction with the help of two-way light-like connection. Corresponding causality connection descriptive-geometric interpreted as a closed a figure “eight” loop light-like curve, from the quantum point of view – as symmetrical T – time jump-reflection between the “nearest” local past and future. Discrete character of the constructed “quantum proximity” equation, containing gravitational constant, is connected with the existence of the local curvature on the Planck scale. Algebraic closure of the basic equation leads to, that E(6) – group becomes the charge symmetry group with nonstandard representations for the fermion and scalar fields. Also the model allows to consider symmetric two-way time stream as a chain of local T reflections. Based on the calculated U expression effective superinvariant Lagrangian with fixed coefficients close to the Planck scale is proposed. This Lagrangian makes possible to take low-energy limit for the comparison with the real world.