On Batalin-Vilkovisky Formalism of Non-Commutative Field Theories

TL;DR

This paper applies the Batalin-Vilkovisky formalism to non-commutative field theories, introduces BRST symmetry, and explores gauge fixing, revealing reducible gauge algebras and analyzing specific models.

Contribution

It extends the BV formalism to non-commutative models, highlighting the complexity of gauge symmetries and providing a detailed example with the Connes-Lott model.

Findings

Gauge symmetries can be reducible in non-commutative models

Application of BV formalism to specific non-commutative models

Derivation of a superversion of the Harish-Chandra-Itzykson-Zuber integral

Abstract

We apply the BV formalism to non-commutative field theories, introduce BRST symmetry, and gauge-fix the models. Interestingly, we find that treating the full gauge symmetry in non-commutative models can lead to reducible gauge algebras. As one example we apply the formalism to the Connes-Lott two-point model. Finally, we offer a derivation of a superversion of the Harish-Chandra-Itzykson-Zuber integral.