Spontaneous Symmetry Breaking in Twisted Noncommutative Quantum Theories

TL;DR

This paper investigates spontaneous symmetry breaking in twisted noncommutative quantum field theories on Moyal spacetimes, developing a scattering formalism compatible with twisted Poincaré symmetry and deriving Goldstone's theorem.

Contribution

It introduces an LSZ formalism for Moyal spacetimes that accounts for symmetry breaking and derives Goldstone's theorem in this noncommutative setting.

Findings

Scattering amplitudes on Moyal spacetime relate to commutative case

Goldstone's theorem holds in twisted noncommutative theories

Formalism applicable to twisted standard model

Abstract

We analyse aspects of symmetry breaking for Moyal spacetimes within a quantisation scheme which preserves the twisted Poincar\'e symmetry. Towards this purpose, we develop the LSZ approach for Moyal spacetimes. The latter gives a formula for scattering amplitudes on these spacetimes which can be obtained from the corresponding ones on the commutative spacetime. This formula 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.