Abstract
We study two different possibilities of constructing the energy-momentum tensors for non-commutative Abelian Proca field, by using (i) general Noether theorem and (ii) coupling to a weak external gravitational field. Both energy-momentum tensors are not traceless due to the violation of Lorentz invariance in non-commutative spaces. In particular, we show that the obtained energy density of the latter case coincides exactly with that of obtained by Dirac quantization method.
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