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About dimensional regularization in the Yang–Mills theory
Zapiski Nauchnykh Seminarov POMI, Questions of quantum field theory and statistical physics. Part 24, Tome 465 (2017), pp. 147-156 Cet article a éte moissonné depuis la source Math-Net.Ru

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In the work the asymptotic approach is proposed for the renormalization in the case of dimensional regularization. As an example, the quantum Yang–Mills theory in the four-dimensional space-time is considered. The formula for the renormalized effective action is derived by using the asymptotic behavior of the bare coupling constant. Then the dimensional transmutation, the process of renormalization and the properties of the coupling constant are discussed. 
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     author = {A. V. Ivanov},
     title = {About dimensional regularization in the {Yang{\textendash}Mills} theory},
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     year = {2017},
     volume = {465},
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     url = {http://geodesic.mathdoc.fr/item/ZNSL_2017_465_a8/}
}
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A. V. Ivanov. About dimensional regularization in the Yang–Mills theory. Zapiski Nauchnykh Seminarov POMI, Questions of quantum field theory and statistical physics. Part 24, Tome 465 (2017), pp. 147-156. http://geodesic.mathdoc.fr/item/ZNSL_2017_465_a8/

[1] G. 't Hooft, M. Veltman, Nucl. Phys. B, 44 (1972), 189–213 | DOI

[2] C. G. Bollini, J. J. Giambiaggi, Phys. Lett. B, 40 (1972), 566–568 | DOI

[3] S. E. Derkachev, A. V. Ivanov, L. D. Faddeev, Theoret. and Math. Phys., 192:2 (2017), 1134–1140 | DOI | MR | Zbl

[4] J. Zinn-Justin, Quantum Field Theory and Critical Phenomena, Clarendon Press, 2002 | MR

[5] S. Weinberg, The Quantum Theory of Fields, Cambridge University Press, 1999 | MR

[6] N. N. Bogolyubov, D. V. Shirkov, Vvedenie v teoriyu kvantovannykh polei, Nauka, M., 1984 | MR

[7] L. D. Faddeev, A. A. Slavnov, Gauge Fields: Introduction To Quantum Theory, Front. Phys., 50, 1980 | MR | Zbl

[8] L. D. Faddeev, Int. J. Mod. Phys. A, 31 (2016), 1630001 | DOI | MR | Zbl

[9] L. D. Faddeev, Theoret. and Math. Phys., 148:1 (2006), 986–994 | DOI | MR | Zbl

[10] David J. Gross, “Applications of the Renormalization Group to High-Energy Physics”, Methods in Field Theory, Les Houches Session XXVIII, 1981, 141–250

[11] F. Olness, R. Scalise, American Journal of Physics, 79 (2011), 306–312 | DOI

[12] A. V. Ivanov, EPJ Web of Conferences, 158 (2017), 07004 | DOI

[13] V. Fock, Phys. Z. Sowjetunion, 12 (1937), 404–425 | Zbl

[14] L. D. Faddeev, Mass in Quantum Yang–Mills Theory: Comment on a Clay Millenium problem, 2009, arXiv: 0911.1013[math-ph] | MR

[15] I. Y. Arefeva, L. D. Faddeev, A. A. Slavnov, Theor. Math. Phys., 21:3 (1974), 1165–1172 | DOI