---
abstract: 'We analyse aspects of symmetry breaking for Moyal spacetimes within a quantisation scheme which preserves the twisted Poincaré 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.'
author:
- 'A. P. Balachandran[^1]'
- 'T. R. Govindarajan[^2]'
- 'Sachindeo Vaidya[^3]'
title: |
    [IISc-CHEP/01/09]{}\
    [IMSC-2009/01/01]{}\
    [SU-4252-883]{}\
    Spontaneous Symmetry Breaking In Twisted Noncommutative Quantum Theories
---

Introduction
============

Spontaneous breaking of a continuous symmetry involves a subtle interplay between an infinite number of degrees of freedom, local and spacetime symmetries, dimension of spacetime, and the notion of (non-)locality of interaction. Naturally one would suspect that the phenomenon of spontaneous symmetry breaking (SSB) leads to different physics in the context of quantum field theories on the Groenewold-Moyal (GM) plane, when the idea of locality is altered, albeit in a very precise sense: pointwise multiplication of two functions is replaced by [*star*]{}-multiplication, which 