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 Cet article a éte moissonné depuis la source Math-Net.Ru

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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. 
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     author = {T. A. Bolokhov},
     title = {Examples of zero modes of the {Faddeev{\textendash}Popov} operator for the $SU(2)$ gauge field},
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     url = {http://geodesic.mathdoc.fr/item/ZNSL_2023_520_a4/}
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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/

[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