A note on the implementation of Poincaré symmetry in noncommutative field theory

Abstract

We argue that Poincaré symmetry can be implemented in NCFT if we allow the parameter of noncommutitive deformation ${\theta }^{\mu \nu }$ to change as a two-tensor under the corresponding space-time symmetry. The implementation is consistent with the definition of ${\theta }^{\mu \nu }$ in terms of space-time coordinates and with the Moyal star product. Inspired from the standard definition of a variational symmetry we found a universal way to correct the implementation of the Poincaré symmetry by a term proportional to the variation of ${\theta }^{\mu \nu }$ in such a way that the new transformation define a symmetry of the theory. Finally we present as an example the case of NCYM theory and comment about the obstructions to implement generalized space-time symmetries in NCFT like conformal or diffeomorphism transformations.

22 pages.

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• A Gravity Theory on Noncommutative Spaces
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Cited by in corpus (1)

• Seiberg-Witten Map with Lorentz-Invariance and Gauge-Covariant Star Product