, Volume 8, Issue 3, pp 427-474,
Open Access This content is freely available online to anyone, anywhere at any time.
Date: 18 May 2007

Renormalization of the Orientable Non-commutative Gross–Neveu Model

Abstract.

We prove that the non-commutative Gross–Neveu model on the two-dimensional Moyal plane is renormalizable to all orders. Despite a remaining UV/IR mixing, renormalizability can be achieved. However, in the massive case, this forces us to introduce an additional counterterm of the form \(\bar{\psi}\imath\gamma^{0}\gamma^{1}\psi\). The massless case is renormalizable without such an addition.