The energy-momentum tensor on noncommutative spaces - some pedagogical comments

TL;DR

This paper explores the properties of the energy-momentum tensor in noncommutative scalar field theories, analyzing symmetries and conservation laws using operator-level methods and classical considerations.

Contribution

It provides a pedagogical discussion of the energy-momentum tensor in noncommutative spaces, including the Noether procedure and symmetry breaking analysis.

Findings

Operator-level Noether procedure applied to noncommutative scalar theory

Analysis of broken dilatation symmetry at the classical level

Insights into energy-momentum tensor structure in noncommutative geometry

Abstract

We present the discussion of the energy-momentum tensor of the scalar $\phi^4$- theory on a noncommutative space. The Noether procedure is performed at the operator level. Additionally, the broken dilatation symmetry will be considered in a Moyal-Weyl deformed scalar field theory at the classical level.