Wavelet regularization of gauge theories

Abstract

Extending the principle of local gauge invariance $\psi (x)\to \exp \left(ı{\sum }_A{\omega }^A(x)T^A\right)\psi (x),x\in {\mathbb{R}}^d$, with $T^A$ being the generators of the gauge group $\mathcal{A}$, to the fields $\psi (g)\equiv ⟨\chi |{\Omega }^{\ast }(g)|\psi ⟩$, defined on a locally compact Lie group $G$, $g\in G$, where $\Omega (g)$ is suitable square-integrable representation of $G$, it is shown that taking the coordinates ($g$) on the affine group, we get a gauge theory that is finite by construction. The renormalization group in the constructed theory relates to each other the charges measured at different scales. The case of the $\mathcal{A}=SU(N)$ gauge group is considered.

15 LaTeX pages, 8 figures

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