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

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.