Renormalization on noncommutative torus D. D'Ascanio, P. Pisani, D. V. Vassilevich
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ArticleSubject(s): однопетлевая перенормировка | квантовая теория поляGenre/Form: статьи в журналах Online resources: Click here to access online
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The European physical journal C Vol. 76, № 4. P. 180 (1-11)Abstract: We study a self-interacting scalar φ4 theory on the d-dimensional noncommutative torus. We determine, for the particular cases d=2 and d=4, the counterterms required by one-loop renormalization. We discuss higher loops in two dimensions and two-loop contributions to the self-energy in four dimensions. Our analysis points toward the absence of any problems related to the ultraviolet/infrared mixing and thus to renormalizability of the theory. However, we find another potentially troubling phenomenon which is a wild behavior of the two-point amplitude as a function of the noncommutativity matrix θ.
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We study a self-interacting scalar φ4 theory on the d-dimensional noncommutative torus. We determine, for the particular cases d=2 and d=4, the counterterms required by one-loop renormalization. We discuss higher loops in two dimensions and two-loop contributions to the self-energy in four dimensions. Our analysis points toward the absence of any problems related to the ultraviolet/infrared mixing and thus to renormalizability of the theory. However, we find another potentially troubling phenomenon which is a wild behavior of the two-point amplitude as a function of the noncommutativity matrix θ.
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