Representation of the \(\beta\)-function and anomalous dimensions by nonsingular integrals in models of critical dynamics. (English. Russian original) Zbl 1336.81063
Theor. Math. Phys. 185, No. 1, 1361-1369 (2015); translation from Teor. Mat. Fiz. 185, No. 1, 3-11 (2015).
Summary: We propose a method for calculating the \(\beta\)-function and anomalous dimensions in critical dynamics models that is convenient for numerical calculations in the framework of the renormalization group and \(\varepsilon\)-expansion. Those quantities are expressed in terms of the renormalized Green’s function, which is renormalized using the operation R represented in a form that allows reducing ultraviolet divergences of Feynman diagrams explicitly. The integrals needed for the calculation do not contain poles in \(\varepsilon\) and are convenient for numerical integration.
MSC:
| 81T17 | Renormalization group methods applied to problems in quantum field theory |
| 81T18 | Feynman diagrams |
| 35B33 | Critical exponents in context of PDEs |
| 33B15 | Gamma, beta and polygamma functions |
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