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

TL;DR

This paper introduces a novel 2D noncommutative 3-colour scalar quantum field theory model, deriving a unique Ward-Takahashi identity and solving the resulting equations perturbatively, advancing understanding of noncommutative QFTs.

Contribution

It presents the first formulation of a 3-colour noncommutative scalar QFT in 2D, with a new Ward-Takahashi identity and a perturbative solution to the 2-point function.

Findings

Derived a generalized Ward-Takahashi identity specific to coloured noncommutative QFTs.

Simplified Schwinger-Dyson equations using the new identity.

Solved the recursive integral equation for the 2-point function up to sixth order.

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 and has no underlying continuous symmetry. 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 $(\mathcal{N},V)$-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.