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

Alexander Hock, Raimar Wulkenhaar
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;%%" }