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arXiv · 0806.3886

One-loop $β$ functions of a translation-invariant renormalizable noncommutative scalar model

Joseph Ben Geloun·Adrian Tanasa
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Abstract

Recently, a new type of renormalizable $ϕ^{\star 4}_{4}$ scalar model on the Moyal space was proved to be perturbatively renormalizable. It is translation-invariant and introduces in the action a $a/(θ^2p^2)$ 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 behaviour as the one of the $ϕ^4$ 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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Joseph Ben Geloun, Adrian Tanasa. 2008-09-15. One-loop $β$ functions of a translation-invariant renormalizable noncommutative scalar model. https://doi.org/10.1007/s11005-008-0270-7

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