We describe the application of the continuous wavelet transform to calculation of the Green functions in quantum field theory. The method of continuous wavelet transform in quantum field theory consists in substitution of the local fields u(x) by those dependent on both the position (x) and the resolution (a) in the action of a field theory model: S=S[u(a,x)]. Since all physical measurement can be performed at a finite resolution only, (a>0), all n-point Green functions in wavelet-based models turn to be finite by construction, provided by the causality condition there should be no scales in internal lines of Feynman diagrams smaller than the measurement scale. The renormalization group, with respect to scale argument a, turns to be a symmetry group in a theory initially formulated in a space of scale-dependent functions u(a,x). The effective action Г[A] of our theory turns to be complementary to the exact renormalization group effective action. The role of the regulator is played by the basic wavelet - an ''aperture function'' of a measuring device used to produce the snapshot of a field u with the resolution a.
1. M.V.Altaisky, Unifying renormalization group and the continuous wavelet transform, Phys. Rev. D 93(2016)105043
2. M.V.Altaisky and N.E.Kaputkina, Continuous wavelet transform in quantum field theory, Phys. Rev. D 88 (2013) 025015
3. F.Bulut and W.Polyzou, Wavelets in
field theory, Phys. Rev. D 87 (2013) 116011
4. M.V.Altaisky, Quantum field theory without divergences, Phys. Rev. D 81 (2010) 125003
5. G. Battle, Wavelets and renormalization group, World Scientific,1999.
contact mail: email@example.com