Eur. Phys. J. C (2018) 78: 580
https://doi.org/10.1140/epjc/s10052-018-6042-3

Regular Article - Theoretical Physics

Noncommutative 3-colour scalar quantum field theory model in 2D

Mathematisches Institut der Westfälischen, Wilhelms-Universität, Einsteinstraße 62, 48149, Münster, Germany

^* e-mail: a_hock03@uni-muenster.de

Received: 30 April 2018
Accepted: 2 July 2018
Published online: 18 July 2018

Abstract

We introduce the 3-colour noncommutative quantum field theory model in two dimensions. For this model we prove a generalised Ward–Takahashi identity, which is special to coloured noncommutative QFT models. It reduces to the usual Ward–Takahashi identity in a particular case. The Ward–Takahashi identity is used to simplify the Schwinger–Dyson equations for the 2-point function and the N-point function. The absence of any renormalisation conditions in the large -limit in 2D leads to a recursive integral equation for the 2-point function, which we solve perturbatively to sixth order in the coupling constant.