Twisted Grosse-Wulkenhaar $\phi^{\star 4}$ model: dynamical noncommutativity and Noether currents

TL;DR

This paper derives explicit expressions for Noether currents in a renormalizable noncommutative Grosse-Wulkenhaar $\,\phi^{\star 4}$ model with dynamical noncommutativity, maintaining invariance through a specific constraint.

Contribution

It provides the first explicit derivation of energy-momentum, angular momentum, and dilatation currents in a dynamical noncommutative field theory with twisted Moyal product.

Findings

Explicit forms of noncommutative energy-momentum tensor, angular momentum tensor, and dilatation current.

Avoidance of invariance breaking via a constraint equation.

Analysis of how dynamical noncommutativity affects conserved currents.

Abstract

This paper addresses the computation of Noether currrents for the renormalizable Grosse-Wulkenhaar (GW) $\phi^{\star 4}$ model subjected to a dynamical noncomutativity realized through a twisted Moyal product. The noncommutative (NC) energy-momentum tensor (EMT), angular momentum tensor (AMT) and the dilatation current (DC) are explicitly derived. The breaking of translation and rotation invariances has been avoided via a constraint equation.