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

Abstract

This paper addresses the computation of Noether currrents for the renormalizable Grosse-Wulkenhaar (GW) ${\varphi }^{\star 4}$ 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.

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• Renormalization of the commutative scalar theory with harmonic term to all orders
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• Energy momentum tensor for translation invariant renormalizable noncommutative field theory