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Theoretical and Mathematical Physics

, Volume 192, Issue 2, pp 1134–1140 | Cite as

Renormalization scenario for the quantum Yang–Mills theory in four-dimensional space–time

  • C. E. Derkachev
  • A. V. Ivanov
  • L. D. Faddeev
Article

Abstract

We consider the renormalization of the Yang–Mills theory in four-dimensional space–time using the background-field formalism.

Keywords

quantum theory of Yang–Mills fields effective action renormalization 

References

  1. 1.
    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).ADSMathSciNetCrossRefMATHGoogle Scholar
  2. 2.
    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).ADSCrossRefMATHGoogle Scholar
  3. 3.
    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.Google Scholar
  4. 4.
    L. F. Abbott, “Introduction to the background field method,” Acta Phys. Polon. B, 13, 33–50 (1982).MathSciNetGoogle Scholar
  5. 5.
    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).CrossRefGoogle Scholar
  6. 6.
    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).MATHGoogle Scholar
  7. 7.
    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).MathSciNetCrossRefMATHGoogle Scholar
  8. 8.
    V. Fock, “Proper time in classical and quantum mechanics,” Phys. Z. Sowjetunion, 12, 404–425 (1937).MATHGoogle Scholar

Copyright information

© Pleiades Publishing, Ltd. 2017

Authors and Affiliations

  • C. E. Derkachev
    • 1
  • A. V. Ivanov
    • 1
  • L. D. Faddeev
    • 1
  1. 1.St. Petersburg Department of the Steklov Institute of Mathematics of the Russian Academy of SciencesSt. PetersburgRussia

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