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arXiv · 1804.06075

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

Alexander Hock·Raimar Wulkenhaar
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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.

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Alexander Hock, Raimar Wulkenhaar. 2018-06-18. Noncommutative 3-colour scalar quantum field theory model in 2D. https://doi.org/10.1140/epjc%2Fs10052-018-6042-3

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