Geodesic
Examples of zero modes of the Faddeev–Popov operator for the $SU(2)$ gauge field
Zapiski Nauchnykh Seminarov POMI, Questions of quantum field theory and statistical physics. Part 29, Tome 520 (2023), pp. 139-150 
T. A. Bolokhov. Examples of zero modes of the Faddeev–Popov operator for the $SU(2)$ gauge field. Zapiski Nauchnykh Seminarov POMI, Questions of quantum field theory and statistical physics. Part 29, Tome 520 (2023), pp. 139-150. http://geodesic.mathdoc.fr/item/ZNSL_2023_520_a4/
@article{ZNSL_2023_520_a4,
     author = {T. A. Bolokhov},
     title = {Examples of zero modes of the {Faddeev{\textendash}Popov} operator for the $SU(2)$ gauge field},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {139--150},
     year = {2023},
     volume = {520},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2023_520_a4/}
}
TY  - JOUR
AU  - T. A. Bolokhov
TI  - Examples of zero modes of the Faddeev–Popov operator for the $SU(2)$ gauge field
JO  - Zapiski Nauchnykh Seminarov POMI
PY  - 2023
SP  - 139
EP  - 150
VL  - 520
UR  - http://geodesic.mathdoc.fr/item/ZNSL_2023_520_a4/
LA  - ru
ID  - ZNSL_2023_520_a4
ER  - 
%0 Journal Article
%A T. A. Bolokhov
%T Examples of zero modes of the Faddeev–Popov operator for the $SU(2)$ gauge field
%J Zapiski Nauchnykh Seminarov POMI
%D 2023
%P 139-150
%V 520
%U http://geodesic.mathdoc.fr/item/ZNSL_2023_520_a4/
%G ru
%F ZNSL_2023_520_a4

Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

We construct zeros of the Faddeev–Popov operator for the $SU(2)$ gauge field in the Coulomb gauge parametrized by expressions with a simple interaction of components of spacial and internal symmetries. The radial component of the gauge field is taken in the form of rational expression with negative poles of the first and the second order.

[1] V. N. Popov, L. D. Faddeev, Teoriya vozmuschenii dlya kalibrovochno-invariantnykh polei, Preprint ITF-67-036, Kiev, 1967

[2] J. Schwinger, “Non-Abelian gauge fields. Relativistic invariance”, Phys. Rev., 127 (1962), 324–330 | DOI | MR | Zbl

[3] N. H. Christ, T. D. Lee, “Operator ordering and Feynman rules in Gauge theories”, Phys. Rev. D, 22 (1980), 970–972 | DOI | MR

[4] V. N. Gribov, “Quantization of non-Abelian gauge theories”, Nucl. Phys. B, 139 (1978), 1–19 | DOI | MR

[5] F. Henyey, “Gribov ambiguity without topological charge”, Phys. Rev. D, 20 (1979), 1460 | DOI

[6] A. Ilderton, M. Lavelle, D. McMullan, “Colour, copies and confinement”, JHEP, 0703 (2007), 044, arXiv: hep-th/0701168 | DOI | MR

[7] R. R. Landim, L. C. Q. Vilar, O. S. Ventura, V. E. R. Lemes, “On the zero modes of the Faddeev-Popov operator in the Landau gauge”, J. Math. Phys., 55 (2014), 022901 | DOI | MR | Zbl

[8] R. D. Rikhtmaier, Printsipy sovremennoi matematicheskoi fiziki, v. 1, Mir, M., 1982 | MR

[9] F. Olver, Asimptotika i spetsialnye funktsii, Nauka, M., 1990

[10] E. Hille, Ordinary differential equations in the complex domain, Dover Books on Mathematics, 1976, 374–401 | MR

[11] A. B. Olde Daalhuis, Hypergeometric function, NIST Handbook of Mathematical Functions, eds. F. W. J. Olver, D. M. Lozier, R. F. Boisvert, C. W. Clark, Cambridge University Press | MR