
Symmetry in Nonlinear Mathematical Physics  2009
George Stavraki (Dorodnicyn Computing Centre of the Russian Academy of Sciences, Moscow, Russia)
Quantum model of geometrical extension
Abstract:
Based on the idea about the identity of spacetime 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 spingroup basises in the Fermifields
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 twoway lightlike
connection. Corresponding causality connection descriptivegeometric interpreted as a closed a figure “eight” loop lightlike curve,
from the quantum point of view – as symmetrical
T – time jumpreflection 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 twoway 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 lowenergy limit for the comparison with the real world.

