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.

arXiv comment17 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

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Cited by in corpus (8)

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• Symplectic Dirac Equation
• Gauging the higher-spin-like symmetries by the Moyal product
• $\kappa$-General-Relativity I: a Non-Commutative GR Theory with the $\kappa$-Minkowski Spacetime as its Flat Limit
• Field Theory with Coordinate Dependent Noncommutativity
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• A Quantum Energy Inequality for a Non-commutative QFT
• Electromagnetic Theory with Quantum Principal Bundles