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

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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. 
@article{ZNSL_2023_520_a4,
     author = {T. A. Bolokhov},
     title = {Examples of zero modes of the {Faddeev--Popov} operator for the $SU(2)$ gauge field},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {139--150},
     publisher = {mathdoc},
     volume = {520},
     year = {2023},
     language = {ru},
     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/