SL(2,R)-Symmetry and Noncommutative Phase Space in (2+2) Dimensions

TL;DR

This paper explores the extension of 2t physics to (2+2) dimensions, revealing a noncommutative algebraic structure linked to SL(2,R) symmetry and discussing potential connections to nonsymmetric gravity theories.

Contribution

It introduces a formalism connecting 2t physics with noncommutative geometry in (2+2) dimensions, highlighting an algebra related to $U_{\star}(1,1)$ and SL(2,R).

Findings

Derived a generalized SL(2,R)-Hamiltonian algebra in (2+2) dimensions.

Identified a noncommutative group structure $U_{\star}(1,1)$.

Discussed potential links to nonsymmetric gravitational theories.

Abstract

We generalize the connection between 2t physics and noncommutative geometry. In particular, we apply our formalism to a target spacetime of signature (2+2). Specifically, we compute an algebra of a generalized SL(2, R)-Hamiltonian constraint, showing that it satisfies a kind of algebra associated with the noncommutative group $U_{\star}(1,1)$. We also comment about a possible connection between our formalism and nonsymmetric gravitational theory.