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TMF, 2001, Volume 128, Number 3, Pages 409–421 (Mi tmf505)  

This article is cited in 2 scientific papers (total in 2 papers)

Conformally Invariant Regularization and Skeleton Expansions in Gauge Theory

V. N. Zaikina, M. Ya. Pal'chikb

a P. N. Lebedev Physical Institute, Russian Academy of Sciences
b Institute of Automation and Electrometry, Siberian Branch of Russian Academy of Sciences

Abstract: We consider a conformally invariant regularization of an Abelian gauge theory in an Euclidean space of even dimension $D\geq4$ and regularized skeleton expansions for vertices and higher Green's functions. We set the respective regularized fields $A^\varepsilon_\mu$ and $j^\varepsilon_\mu$ with the scaling dimensions $l^\varepsilon_A=1-\varepsilon$, and $l^\varepsilon_j=D-1+\varepsilon$ into correspondence to the gauge field $A_\mu$ and Euclidean current $j_\mu$. We postulate special rules for the limiting transition $\varepsilon\to0$. These rules are different for the transversal and longitudinal components of the field $A^\varepsilon_\mu$ and the current $j^\varepsilon_\mu$. We show that in the limit $\varepsilon\to0$, there appear conformally invariant fields $A_\mu$ and $j_\mu$ each of which is transformed by a direct sum of two irreducible representations of the conformal group. Removing the regularization, we obtain a well-defined skeleton theory constructed from conformal two- and three-point correlation functions. We consider skeleton equations on the transversal component of the vertex operator and of the spinor propagator in conformal quantum electrodynamics. For simplicity, we restrict the consideration to an Abelian gauge field $A_\mu$, but generalization to a non-Abelian theory is straightforward.

DOI: https://doi.org/10.4213/tmf505

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English version:
Theoretical and Mathematical Physics, 2001, 128:3, 1181–1192

Bibliographic databases:

Received: 20.04.2001

Citation: V. N. Zaikin, M. Ya. Pal'chik, “Conformally Invariant Regularization and Skeleton Expansions in Gauge Theory”, TMF, 128:3 (2001), 409–421; Theoret. and Math. Phys., 128:3 (2001), 1181–1192

Citation in format AMSBIB
\Bibitem{ZaiPal01}
\by V.~N.~Zaikin, M.~Ya.~Pal'chik
\paper Conformally Invariant Regularization and Skeleton Expansions in Gauge Theory
\jour TMF
\yr 2001
\vol 128
\issue 3
\pages 409--421
\mathnet{http://mi.mathnet.ru/tmf505}
\crossref{https://doi.org/10.4213/tmf505}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1902851}
\zmath{https://zbmath.org/?q=an:1040.81065}
\transl
\jour Theoret. and Math. Phys.
\yr 2001
\vol 128
\issue 3
\pages 1181--1192
\crossref{https://doi.org/10.1023/A:1012355602048}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000172327200006}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Delbourgo, R, “Self-consistent nonperturbative anomalous dimensions”, Journal of Physics A-Mathematical and General, 36:46 (2003), 11697  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    2. Delbourgo, R, “Nonperturbative characteristics of Green functions”, Nuclear Physics B-Proceedings Supplements, 141 (2005), 63  crossref  adsnasa  isi  elib  scopus  scopus
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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