Geodesic
Zero modes of the Laplace operator in two-loop calculations in the Yang--Mills theory
Zapiski Nauchnykh Seminarov POMI, Questions of quantum field theory and statistical physics. Part 28, Tome 509 (2021), pp. 216-226

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In this paper we study two-loop calculations in the Yang–Mills theory. Using the heat kernel method we construct two Green functions and add contributions to them, corresponding to the zero modes of the Laplace operator. We show by the direct calculations that such additions do not affect the second coefficient of the $\beta$-function in the Yang–Mills theory. 
@article{ZNSL_2021_509_a13,
     author = {N. V. Kharuk},
     title = {Zero modes of the {Laplace} operator in two-loop calculations in the {Yang--Mills} theory},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {216--226},
     publisher = {mathdoc},
     volume = {509},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2021_509_a13/}
}
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N. V. Kharuk. Zero modes of the Laplace operator in two-loop calculations in the Yang--Mills theory. Zapiski Nauchnykh Seminarov POMI, Questions of quantum field theory and statistical physics. Part 28, Tome 509 (2021), pp. 216-226. http://geodesic.mathdoc.fr/item/ZNSL_2021_509_a13/