Abstract
The principle of symmetry with respect to local gauge transformations \(\psi (x) \to {{e}^{{\imath w(x)}}}\psi (x)\) has been extended to fields \(\psi (g) \equiv \left\langle {\chi \left| {\Omega {\kern 1pt} *{\kern 1pt} (g)} \right|\psi } \right\rangle \) defined on a locally compact Lie group \(g \in G\), where \(\Omega (g)\) is a square-integrable representation of \(G\). It has been shown that if \(G\) is an affine group \(G:x{\kern 1pt} ' = ax + b,x,b \in {{\mathbb{R}}^{d}}\), one can construct a quantum field model with a gauge group \(SU(N)\) that is free of both UV and IR divergences.
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ACKNOWLEDGMENTS
The author is grateful to A.V. Bednyakov, S.V. Mikhailov, and O.V. Tarasov for useful discussions.
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Translated by V. Arutyunyan
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Altaisky, M.V. Multiscale Gauge Invariance. Phys. Part. Nuclei 51, 521–525 (2020). https://doi.org/10.1134/S1063779620040061
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DOI: https://doi.org/10.1134/S1063779620040061