Abstract
Recently, a new type of renormalizable \({\phi^{\star 4}_{4}}\) scalar model on the Moyal space was proved to be perturbatively renormalizable. It is translation-invariant and introduces in the action a a/(θ 2 p 2) term. We calculate here the β and γ functions at one-loop level for this model. The coupling constant β λ function is proved to have the same behavior as the one of the \({\phi^4}\) model on the commutative \({\mathbb{R}^4}\) . The β a function of the new parameter a is also calculated. Some interpretation of these results are done.
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Geloun, J.B., Tanasa, A. One-Loop β Functions of a Translation-Invariant Renormalizable Noncommutative Scalar Model. Lett Math Phys 86, 19–32 (2008). https://doi.org/10.1007/s11005-008-0270-7
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DOI: https://doi.org/10.1007/s11005-008-0270-7