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

April 17, 2018

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.

Keywords:

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