Continuous Wavelet Transform in Quantum Field Theory

Abstract

We describe the application of the continuous wavelet transform to calculation of the Green functions in quantum field theory: scalar ${\varphi }^4$ theory, quantum electrodynamics, quantum chromodynamics. The method of continuous wavelet transform in quantum field theory presented in M.Altaisky Phys. Rev. D81(2010)125003 for the scalar ${\varphi }^4$ theory, consists in substitution of the local fields $\varphi (x)$ by those dependent on both the position $x$ and the resolution $a$. The substitution of the action $S[\varphi (x)]$ by the action $S[{\varphi }_a(x)]$ makes the local theory into nonlocal one, and implies the causality conditions related to the scale $a$, the region causality J.D. Christensen and L. Crane, J.Math. Phys 46 (2005) 122502. These conditions make the Green functions $G(x_1,a_1,...,x_n,a_n)=<{\varphi }_{a_1}(x_1)...{\varphi }_{a_n}(x_n)>$ finite for any given set of regions by means of an effective cutoff scale $A=\min (a_1,...,a_n)$.

15 pages, RevTex, 8 eps figures

References in corpus (2)

• Wavelet-Based Quantum Field Theory
• Field on Poincare group and quantum description of orientable objects

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