Noncommutative Extension of Minkowski Spacetime and Its Primary Application

TL;DR

This paper introduces a noncommutative extension of Minkowski spacetime using a proper time concept, enabling the construction of noncommutative field theories with inherent temporal fuzziness and analyzing chiral bosons within this framework.

Contribution

It presents a novel noncommutative Minkowski spacetime model based on proper time, facilitating natural incorporation of noncommutative effects into field theories.

Findings

Constructed a commutative spacetime encoding noncommutativity via proper time.

Developed noncommutative chiral boson models and their quantization.

Analyzed self-duality of the models using the parent action approach.

Abstract

We propose a noncommutative extension of the Minkowski spacetime by introducing a well-defined proper time from the kappa-deformed Minkowski spacetime related to the standard basis. The extended Minkowski spacetime is commutative, i.e. it is based on the standard Heisenberg commutation relations, but some information of noncommutativity is encoded through the proper time to it. Within this framework, by simply considering the Lorentz invariance we can construct field theory models that comprise noncommutative effects naturally. In particular, we find a kind of temporal fuzziness related to noncommutativity in the noncommutative extension of the Minkowski spacetime. As a primary application, we investigate three types of formulations of chiral bosons, deduce the lagrangian theories of noncommutative chiral bosons and quantize them consistently in accordance with Dirac's method, and further analyze the self-duality of the lagrangian theories in terms of the parent action approach.