Wavelets and renormalization group in quantum field theory problems

Using continuous wavelet transform it is possible to construct a regularization procedure for scale-dependent quantum field theory models, which is complementary to functional renormalization group method in the sense that it sums up the fluctuations of larger scales in order to get the effective action at small observation scale (M.V.Altaisky, Phys. Rev. D93(2016) 105043. The standard RG results for ${\varphi }^4$ model are reproduced. The fixed points of the scale-dependent theory are studied in one loop approximation.