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 TMF, 1986, Volume 67, Number 1, Pages 76–88 (Mi tmf4922)

Conformal invariance in gauge theories II. Yang–Mills theory

R. P. Zaikov

Abstract: The results of Part I are generalized to the non-Abelian ease. By analogy with conformal QED, in which interaction with a matter field is realized by means of a four-vector potential that transforms in accordance with a direct sum of two nonprincipal representations, the first step in the present paper is the construction of a new formulation of quantum eleetrodynamics, in which the four-vector potential is regarded as an independent variable. Although the potential as a whole transforms in accordance with a principal representation, the corresponding conformally invariant two-point functions have a nonzero transverse part, and the Lagrangian is nondegenerate. In the non-Abelian case, one manifestly conformally invariant gauge condition is found, and the corresponding functional determinant is calculated. It is shown that in the gauge-invariant sector this theory is equivalent to the ordinary theory with conformally noninvariant gauge condition. A local effective Lagrangian is constructed, the Faddeev–Popov “ghost” fields having in this case scale dimension zero. It is shown that this effective Lagrangian has a residual global supersymmetry of Becchi–Rouet–Stora type.

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English version:
Theoretical and Mathematical Physics, 1986, 67:1, 368–375

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Revised: 10.04.1985

Citation: R. P. Zaikov, “Conformal invariance in gauge theories II. Yang–Mills theory”, TMF, 67:1 (1986), 76–88; Theoret. and Math. Phys., 67:1 (1986), 368–375

Citation in format AMSBIB
\Bibitem{Zai86} \by R.~P.~Zaikov \paper Conformal invariance in gauge theories II.~Yang--Mills theory \jour TMF \yr 1986 \vol 67 \issue 1 \pages 76--88 \mathnet{http://mi.mathnet.ru/tmf4922} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=843800} \transl \jour Theoret. and Math. Phys. \yr 1986 \vol 67 \issue 1 \pages 368--375 \crossref{https://doi.org/10.1007/BF01028890} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1986E968100008} 

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This publication is cited in the following articles:
1. R. P. Zaikov, “Conformal invariance in gauge theories. III. Linear gravitation”, Theoret. and Math. Phys., 75:3 (1988), 593–599
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