QFT with Twisted Poincar\'e Invariance and the Moyal Product

TL;DR

This paper explores the effects of twisting Poincare invariance in quantum field theory, demonstrating that twisted and untwisted formulations yield equivalent physical predictions through unitary transformations and phase factors.

Contribution

It constructs a compatible Fock space for twisted symmetry, shows the non-existence of linear covariant fields, and relates twisted fields to untwisted ones via a unitary transformation.

Findings

Twisted and untwisted n-point functions are identical.

Twisted symmetry invariance can be realized with usual or Moyal products.

S-matrix elements differ only by a momentum-dependent phase.

Abstract

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.