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Theoretical and Mathematical Physics

, Volume 181, Issue 3, pp 1638–1642 | Cite as

A couple of methodological comments on the quantum Yang-Mills theory

  • L. D. Faddeev
Article

Abstract

We present methodological proposals regarding the definition of the notion of the effective action, the coupling constant renormalization, and the interpretation of dimensional transmutation. We show that the divergences that arise when quantizing a Yang-Mills field can be eliminated and lead to violation of the scaling invariance of the classical theory.

Keywords

effective action dimensional transmutation 

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References

  1. 1.
    A. A. Slavnov and L. D. Faddeev, Introduction to the Quantum Theory of Gauge Fields [in Russian], Nauka, Moscow (1988); English transl.: Gauge Fields: An Introduction to Quantum Theory (Frontiers Phys., Vol. 83), Westview, Boulder, Colo. (1993).zbMATHGoogle Scholar
  2. 2.
    L. D. Faddeev, Bull. Braz. Math. Soc., n.s., 33, 201–212 (2002); arXiv:0911.1013v1 [math-ph] (2009).CrossRefzbMATHMathSciNetGoogle Scholar
  3. 3.
    L. D. Faddeev, “Separation of scattering and selfaction revisited,” arXiv:1003.4854v1 [hep-th] (2010).Google Scholar
  4. 4.
    L. D. Faddeev, Theor. Math. Phys., 148, 986–994 (2006).CrossRefzbMATHMathSciNetGoogle Scholar
  5. 5.
    V. Fock, Phys. Z. Sowjetunion, 12, 404–425 (1937).Google Scholar
  6. 6.
    I. Jack and H. Osborn, Nucl. Phys. B, 207, 474–504 (1982).ADSCrossRefGoogle Scholar
  7. 7.
    L. D. Faddeev, “Knots as possible excitations of the quantum Yang-Mills fields,” in: Quantum Field Theory and Beyond: Essays in Honor of Wolfhart Zimmermann (E. Seiler, K. Sibold, eds.), World Scientific, Hackensack, N. J. (2008), pp. 156–166; arXiv:0805.1624v1 [hep-th] (2008).Google Scholar

Copyright information

© Pleiades Publishing, Ltd. 2014

Authors and Affiliations

  • L. D. Faddeev
    • 1
    • 2
  1. 1.St. Petersburg Branch of the Steklov Institute for MathematicsRASSt. PetersburgRussia
  2. 2.St. Petersburg State UniversitySt. PetersburgRussia

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