# 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.

open access link
doi:10.1140/epjc/s10052-018-6042-3

@article{Hock:2018wup,
author = "Hock, Alexander and Wulkenhaar, Raimar",
title = "{Noncommutative 3-colour scalar quantum field theory
model in 2D}",
journal = "Eur. Phys. J.",
volume = "C78",
year = "2018",
number = "7",
pages = "580",
doi = "10.1140/epjc/s10052-018-6042-3",
eprint = "1804.06075",
archivePrefix = "arXiv",
primaryClass = "math-ph",
SLACcitation = "%%CITATION = ARXIV:1804.06075;%%"
}

Keywords:

*none*