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.
Cite
@article{arxiv.1502.03765,
title = {On the energy-momentum tensor in Moyal space},
author = {Herbert Balasin and Daniel N. Blaschke and Francois Gieres and Manfred Schweda},
journal= {arXiv preprint arXiv:1502.03765},
year = {2015}
}
Comments
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