Spontaneous breaking of symmetry in Moyal spacetime with twisted Poincar\'e symmetry

TL;DR

This paper investigates spontaneous symmetry breaking in Moyal spacetimes with twisted Poincaré symmetry, developing a formalism that maps scattering amplitudes from commutative spacetime and deriving Goldstone's theorem in this noncommutative setting.

Contribution

It introduces a novel LSZ formalism for Moyal spacetimes and extends Goldstone's theorem to the twisted noncommutative framework.

Findings

Derived a scattering amplitude mapping between commutative and Moyal spacetimes.

Established Goldstone's theorem in the context of twisted Poincaré symmetry.

Provided a formalism applicable to the twisted standard model.

Abstract

After briefly reviewing the gauge symmetry in Moyal spacetimes, we analyse aspects of symmetry breaking within a quantisation program preserving the twisted Poincar\'e symmetry. We develop the LSZ approach for Moyal spacetimes and derive a mapping for scattering amplitudes on these spacetimes from the corresponding ones on the commutative spacetime. This map applies in the presence of spontaneous breakdown of symmetries as well. We also derive Goldstone's theorem on Moyal spacetime. The formalism developed here can be directly applied to the twisted standard model.