Geodesic
Conformally Invariant Regularization and Skeleton Expansions in Gauge Theory
Teoretičeskaâ i matematičeskaâ fizika, Tome 128 (2001) no. 3, pp. 409-421 
V. N. Zaikin; M. Ya. Pal'chik. Conformally Invariant Regularization and Skeleton Expansions in Gauge Theory. Teoretičeskaâ i matematičeskaâ fizika, Tome 128 (2001) no. 3, pp. 409-421. http://geodesic.mathdoc.fr/item/TMF_2001_128_3_a6/
@article{TMF_2001_128_3_a6,
     author = {V. N. Zaikin and M. Ya. Pal'chik},
     title = {Conformally {Invariant} {Regularization} and {Skeleton} {Expansions} in {Gauge} {Theory}},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {409--421},
     year = {2001},
     volume = {128},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2001_128_3_a6/}
}
TY  - JOUR
AU  - V. N. Zaikin
AU  - M. Ya. Pal'chik
TI  - Conformally Invariant Regularization and Skeleton Expansions in Gauge Theory
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 2001
SP  - 409
EP  - 421
VL  - 128
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/TMF_2001_128_3_a6/
LA  - ru
ID  - TMF_2001_128_3_a6
ER  - 
%0 Journal Article
%A V. N. Zaikin
%A M. Ya. Pal'chik
%T Conformally Invariant Regularization and Skeleton Expansions in Gauge Theory
%J Teoretičeskaâ i matematičeskaâ fizika
%D 2001
%P 409-421
%V 128
%N 3
%U http://geodesic.mathdoc.fr/item/TMF_2001_128_3_a6/
%G ru
%F TMF_2001_128_3_a6

Voir la notice de l'article provenant de la source Math-Net.Ru

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.

[1] I. T. Todorov, M. G. Mintchev, V. B. Petkova, Conformal Invariance in Quantum Field Theory, Scuola Normale Superiore, Piza, 1978 | MR | Zbl

[2] E. S. Fradkin, M. Ya. Palchik, Conformal Quantum Field Theory in $D$-dimensions, Kluwer Acad. Publishers, Dordrecht, 1996 | MR | Zbl

[3] E. S. Fradkin, M. Ya. Palchik, Phys. Rep., 300 (1998), 1 | DOI | MR

[4] M. Ya. Palchik, J. Phys., 16 (1983), 1523 | DOI

[5] B. Bineger, C. Fronsdal, W. Heidenreich, J. Math. Phys., 24 (1983), 2828 | DOI | MR

[6] R. P. Zaikov, TMF, 65:1 (1985), 70 | MR

[7] P. Furlan, V. B. Petkova, G. M. Sotkov, I. T. Todorov, Nuovo Cim., 8 (1985), 1 | DOI

[8] I. M. Gelfand, M. I. Graev, N. Ya. Vilenkin, Integralnaya geometriya i svyazannye s nei voprosy teorii predstavlenii, Fizmatgiz, M., 1962 | MR

[9] E. S. Fradkin, M. Ya. Palchik, Conformally invariant Green functions of current and energy-momentum tensor in spaces of even dimension $D\geq 4$, E-print hep-th/9712045

[10] V. K. Dobrev, G. Mack, V. B. Petkova, S. G. Petkova, I. T. Todorov, Harmonic Analysis on the $n$-dimensional Lorentz Group and Its Application to Conformal Quantum Field Theory, Lect. Notes Phys., 63, Springer, Berlin, 1977 | Zbl

[11] A. U. Klimyk, Matrichnye elementy i koeffitsienty Klebsha–Gordana predstavlenii grupp, Naukova dumka, Kiev, 1979 | MR | Zbl