Eur. Phys. J. C (2008) 56: 293-304
https://doi.org/10.1140/epjc/s10052-008-0652-0

Regular Article - Theoretical Physics

On the vacuum states for non-commutative gauge theory

¹ Laboratoire de Physique Théorique, Bât. 210, Université Paris XI, 91405, Orsay Cedex, France
² Mathematisches Institut, Westfälische Wilhelms-Universität, Einsteinstraße 62, 48149, Münster, Germany

^* e-mail: jean-christophe.wallet@th.u-psud.fr

Received: 3 April 2008
Published online: 4 July 2008

Abstract

Candidates for renormalizable gauge theory models on Moyal spaces constructed recently have non-trivial vacua. We show that these models support vacuum states that are invariant under both global rotations and symplectic isomorphisms which form a global symmetry group for the action. We compute the explicit expression in position space for these vacuum configurations in two and four dimensions.