Eur. Phys. J. C (2015) 75: 284
https://doi.org/10.1140/epjc/s10052-015-3492-8

Regular Article - Theoretical Physics

On the energy-momentum tensor in Moyal space

¹ Institute for Theoretical Physics, Vienna University of Technology, Wiedner Hauptstraße 8-10, 1040, Vienna, Austria
² Theory Division, Los Alamos National Laboratory, Los Alamos, NM, 87545, USA
³ Institut de Physique Nucléaire de Lyon, Bat. P. Dirac, Université de Lyon, Université Claude Bernard Lyon 1 and CNRS/IN2P3, 4 rue Enrico Fermi, 69622, Villeurbanne, France

^* e-mail: hbalasin@tph.tuwien.ac.at

Received: 18 February 2015
Accepted: 29 May 2015
Published online: 26 June 2015

Abstract

We study the properties of the energy-momentum tensor of gauge fields coupled to matter in non-commutative (Moyal) space. In general, the non-commutativity affects the usual conservation law of the tensor as well as its transformation properties (gauge covariance instead of gauge invariance). It is well known that the conservation of the energy-momentum tensor can be achieved by a redefinition involving another star-product. Furthermore, for a pure gauge theory it is always possible to define a gauge invariant energy-momentum tensor by means of a Wilson line. We show that the last two procedures are incompatible with each other if couplings of gauge fields to matter fields (scalars or fermions) are considered: The gauge invariant tensor (constructed via Wilson line) does not allow for a redefinition assuring its conservation, and vice versa the introduction of another star-product does not allow for gauge invariance by means of a Wilson line.