Comments on the Energy-Momentum Tensor in Non-Commutative Field Theories

TL;DR

This paper examines the properties of the energy-momentum tensor in non-commutative field theories, revealing that it can be non-symmetric and non-traceless, with implications for gauge invariance and conservation laws.

Contribution

It provides a detailed analysis of the energy-momentum tensor's properties in non-commutative scalar and gauge theories, highlighting new forms and conservation features.

Findings

Energy-momentum tensor in non-commutative scalar theory is conserved but non-symmetric.

In massless scalar theories, the tensor is not necessarily traceless.

In gauge theories, a gauge-invariant, conserved tensor can be constructed using Wilson functionals.

Abstract

In a non-commutative field theory, the energy-momentum tensor obtained from the Noether method needs not be symmetric; in a massless theory, it needs not be traceless either. In a non-commutative scalar field theory, the method yields a locally conserved yet non-symmetric energy-momentum tensor whose trace does not vanish for massless fields. A non-symmetric tensor also governs the response of the action to a general coordinate transformation. In non-commutative gauge theory, if translations are suitably combined with gauge transformations, the method yields a covariantly constant tensor which is symmetric but only gauge covariant. Using suitable Wilson functionals, this can be improved to yield a locally conserved and gauge invariant, albeit non-symmetric, energy-momentum tensor.