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Energy-momentum tensors for non-commutative Abelian Proca field
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.Comment: 9 page
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