Operator geometry and algebraic gravity

TL;DR

This paper proposes an algebraic formulation of general relativity applicable to quantum gravity and noncommutative spaces, unifying constraints and evolution equations in operator geometry.

Contribution

It introduces an algebraic canonical formalism for operator geometry, unifying gravitational constraints and evolution, and connects quantum corrections to known quantum field theory results.

Findings

Algebraic formulation applicable to quantum gravity and noncommutative spaces.

Unified constraint and evolution equations in operator geometry.

Quantum corrections match known semi-classical gravity results.

Abstract

An algebraic formulation of general relativity is proposed. The formulation is applicable to quantum gravity and noncommutative space. To investigate quantum gravity we develop the canonical formalism of operator geometry, after reconstructing an algebraic canonical formulation on analytical dynamics. The remarkable fact is that the constraint equation and evolution equation of the gravitational system are algebraically unified. From the discussion of regularization we find the quantum correction of the semi-classical gravity is same as that already known in quantum field theory.