Paper detail

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

We argue that Poincaré symmetry can be implemented in NCFT if we allow the parameter of noncommutitive deformation $θ^{μν}$ to change as a two-tensor under the corresponding space-time symmetry. The implementation is consistent with the definition of $θ^{μν}$ 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 $θ^{μν}$ 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.