Path Integral Approach to Noncommutative Space-Times

TL;DR

This paper introduces a path integral framework for noncommutative spacetime models, incorporating a fundamental length scale, which reduces to classical spacetime in the limit of zero noncommutativity.

Contribution

It presents a novel path integral formulation for noncommutative geometries, extending quantum field theory methods to these generalized spacetime structures.

Findings

Path integral formulation for noncommutative spacetimes established.

Reduction to classical spacetime when noncommutativity parameter approaches zero.

Framework applicable to even-dimensional noncommutative geometries.

Abstract

We propose a path integral formulation of noncommutative generalizations of spacetime manifold in even dimensions, characterized by a length scale $\lambda_P$. The commutative case is obtained in the limit $\lambda_P=0$.