On the energy-momentum tensor in Moyal space

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 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 latter 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.

17 pages; v2: Review of known results on the EMT in Minkowski space removed, results concerning the different matter couplings in Moyal space revised and expanded; to appear in EPJC

References in corpus (3)

• A translation-invariant renormalizable non-commutative scalar model
• Wong's Equations and Charged Relativistic Particles in Non-Commutative Space
• Noether's theorem, the stress-energy tensor and Hamiltonian constraints