We consider the renormalization of the Yang–Mills theory in four-dimensional space–time using the background-field formalism.
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L. D. Faddeev, “Scenario for the renormalization in the 4D Yang–Mills theory,” Internat. J. Modern Phys. A, 31, 1630001 (2016); arXiv:1509.06186v2 [hep-th] (2015).
B. S. DeWitt, “Quantum theory of gravity: II. The manifestly covariant theory,” Phys. Rev., 162, 1195–1239 (1967); “Quantum theory of gravity: III. Applications of the covariant theory,” Phys. Rev., 162, 1239–1256 (1967).
G. ’t Hooft, “The background field method in gauge field theories,” in: Functional and Probabilistic Methods in Quantum Field Theory (Acta Universitatis Wratislaviensis, Vol. 1, No. 368, B. Jancewicz, ed.), Wroclaw Univ., Wroclaw (1976), pp. 345–369.
L. F. Abbott, “Introduction to the background field method,” Acta Phys. Polon. B, 13, 33–50 (1982).
I. Ya. Aref’eva, A. A. Slavnov, and L. D. Faddeev, “Generating functional for the S-matrix in gauge-invariant theories,” Theor. Math. Phys., 21, 1165–1172 (1974).
A. A. Slavnov and L. D. Faddeev, Introduction to the Quantum Theory of Gauge Fields [in Russian], Nauka, Moscow (1978); English transl.: L. D. Faddeev and A. A. Slavnov, Gauge Fields: Introduction to Quantum Theory (Frontiers in Physics, Vol. 50), Benjamin/Cummings, Reading, Mass. (1980).
L. D. Faddeev, “Mass in quantum Yang–Mills theory (comment on a Clay millenium problem),” Bull. Braz. Math. Soc., n.s., 33, 201–212 (2002); arXiv:0911.1013v1 [math-ph] (2009).
V. Fock, “Proper time in classical and quantum mechanics,” Phys. Z. Sowjetunion, 12, 404–425 (1937).
This research is supported by a grant from the Russian Science Foundation (Project No. 14-11-00598).
Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 192, No. 2, pp. 227–234, August, 2017.
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Derkachev, C.E., Ivanov, A.V. & Faddeev, L.D. Renormalization scenario for the quantum Yang–Mills theory in four-dimensional space–time. Theor Math Phys 192, 1134–1140 (2017). https://doi.org/10.1134/S0040577917080049
- quantum theory of Yang–Mills fields
- effective action