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On the energy-momentum tensor in Moyal space

Abstract : After reviewing the known results for the definition and properties of the energy-momentum tensor(s) in Minkowski space, 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 gauge invariant 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.
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Contributor : Sylvie Flores Connect in order to contact the contributor
Submitted on : Thursday, April 16, 2015 - 10:38:09 AM
Last modification on : Friday, September 10, 2021 - 1:50:12 PM

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H. Balasin, D.N. Blaschke, F. Gieres, M. Schweda. On the energy-momentum tensor in Moyal space. European Physical Journal C: Particles and Fields, Springer Verlag (Germany), 2015, 75, pp.284. ⟨10.1140/epjc/s10052-015-3492-8⟩. ⟨in2p3-01142855⟩



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