Space-time as a discrete field noncommutative causal network

TL;DR

This paper proposes a novel discrete, noncommutative model of space-time using operator field theory and algebraic structures, aiming to unify quantum and gravitational phenomena at the Planck scale.

Contribution

It introduces a new noncommutative causal network model of space-time based on operator field complexes and commutator algebra, diverging from traditional manifold-based approaches.

Findings

Defines space-time via physical functions rather than manifolds

Models local events with a universal field supermatrix complex

Suggests a group E_6 symmetry for charge interactions

Abstract

The necessity of rejecting the numerical model of geometrical extension is postulated on the basis of the idea of identity of space-time and physical vacuum. An attempt is made to define space-time not via the concept of manifold, but via the store of physical functions defined on it. The new description is based on the commutator representation of the causal structure of operator field theory. It is not the world point, but a universal field supermatrix complex U that is assumed to be the carrier of possible local events. This complex involves a complete set of Heisenberg local field operators together with their spin-group bases in the Fermi-field representation. The fundamental element of the extension is described in the model by the equation of a special commutator algebra closed on two such local complexes U_1 and U_2 "nearest" in the two-sided light-like connection and linked by a single virtual field interaction vertex. The discrete character of the constructed "quantum proximity" equation containing the gravitational constant is associated with the existence of local curvature on the Planck scale. Algebraic closed-ness of the basic equation suggests that the charge symmetry group should be group E_6 with non-standard representations of the fermion and scalar fields. On the basis of the calculated U expression we propose an effective superinvariant Lagrangian with fixed coefficients on the near-Planck scale, from which one can in principle try to obtain a low-energy limit for comparison with the real world.