Dynamical noncommutativity and Noether theorem in twisted phi^*4 theory

TL;DR

This paper introduces a dynamical noncommutative ^4 theory using a -star product defined by commuting vector fields, deriving conserved quantities and extending the usual Moyal product framework.

Contribution

It presents a novel dynamical -star product in ^4 theory and explicitly derives conserved energy-momentum and angular momentum tensors.

Findings

The -star product reduces to the Moyal product in vacuum.

The theory maintains invariance under rigid translations and Lorentz rotations.

Explicit conserved tensors are derived for the dynamical noncommutative setting.

Abstract

A \star-product is defined via a set of commuting vector fields X_a = e_a^\mu (x) \partial_\mu, and used in a phi^*4 theory coupled to the e_a^\mu (x) fields. The \star-product is dynamical, and the vacuum solution phi =0, e_a^\mu (x)=delta_a^\mu reproduces the usual Moyal product. The action is invariant under rigid translations and Lorentz rotations, and the conserved energy-momentum and angular momentum tensors are explicitly derived.