Wavelet regularization of Euclidean QED

Abstract

The regularization of quantum electrodynamics in the space of functions ${\psi }_a(x)$, which depend on both the position $x$ and the scale $a$, is presented. The scale-dependent functions are defined in terms of the continuous wavelet transform in ${\mathbb{R}}^4$ Euclidean space, with the derivatives of Gaussian served as basic wavelets. The vacuum polarization and the dependence of the effective coupling constant on the scale parameters are calculated in one-loop approximation in the limit $p^2\gg 4m^2$.

19 LaTeX pages, 6 eps figures; to appear in Phys. Rev. D

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