QFT with Twisted Poincaré Invariance and the Moyal Product

Details QFT with Twisted Poincaré Invariance and the Moyal Product QFT with Twisted Poincaré Invariance and the Moyal Product

2007-03-27

arxiv.org/abs/hep-th/0703245v2

JHEP 0705:098,2007

Physics

High Energy Physics

High Energy Physics - Theory

11 pages, references added

Scientific paper

10.1088/1126-6708/2007/05/098

We study the consequences of twisting the Poincare invariance in a quantum field theory. First, we construct a Fock space compatible with the twisting and the corresponding creation and annihilation operators. Then, we show that a covariant field linear in creation and annihilation operators does not exist. Relaxing the linearity condition, a covariant field can be determined. We show that it is related to the untwisted field by a unitary transformation and the resulting n-point functions coincide with the untwisted ones. We also show that invariance under the twisted symmetry can be realized using the covariant field with the usual product or by a non-covariant field with a Moyal product. The resulting S-matrix elements are shown to coincide with the untwisted ones up to a momenta dependent phase.

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