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Theoretical and Mathematical Physics

, Volume 148, Issue 1, pp 986–994 | Cite as

Notes on divergences and dimensional transmutation in Yang—Mills theory

  • L. D. Faddeev
Article

Abstract

We discuss the specificity of charge renormalization in Yang—Mills theory. We show that the values of the running coupling constant in dimensional regularization and in momentum truncation coincide. Dimensional transmutation is interpreted as replacing the dimensionless coupling constant with a dimensional invariant of the renormalization group equation.

Keywords

dimensional transmutation renormalization group equations dimensional regularization momentum truncation 

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References

  1. 1.
    S. Coleman and E. Weinberg, Phys. Rev. D, 7, 1888 (1973).CrossRefADSGoogle Scholar
  2. 2.
    S. P. Merkur’ev and L. D. Faddeev, Quantum Scattering Theory for Several Particle Systems [in Russian], Nauka, Moscow (1985); English transl.: L. D. Faddeev and S. P. Merkuriev, (Math. Phys. Appl. Math., Vol. 11), Kluwer, Dordrecht (1993).Google Scholar
  3. 3.
    F. A. Berezin and L. D. Faddeev, Sov. Math. Dokl., 2, 372 (1961).zbMATHGoogle Scholar
  4. 4.
    R. Jackiw, “What good are quantum field theory infinities,” in: Mathematical Physics 2000 (International Congress, London, GB, 2000, A. Fokas, A. Grigoryan, T. Kibble, and B. Zegarlinski, eds.), Imperial College Press, London (2000), p. 101.Google Scholar
  5. 5.
    G. ’t Hooft, Phys. Stat. Solidi (b), 237, 13 (2003); hep-th/0208054 (2002).CrossRefADSGoogle Scholar
  6. 6.
    F. Wilczek, “Four big questions with pretty good answers,” in: Fundamental Physics: Heisenberg and Beyond (Werner Heisenberg Centennial Symposium “Developments in Modern Physics,” G. W. Buschhorn and J. Wess, eds.), Springer, Berlin (2004), p. 79; hep-ph/0201222 (2002).Google Scholar
  7. 7.
    G. ’t. Hooft, Nucl. Phys. B, 62, 444 (1973); B. S. DeWitt, Dynamic Theory of Groups and Fields, Gordon and Breach, New York (1965).CrossRefADSGoogle Scholar
  8. 8.
    L. D. Faddeev, “Quantum theory of gauge fields,” in: Vector Mesons and Electromagnetic Interactions [in Russian] (Proc. Intl. Seminar, Dubna, 23–26 September 1969, A. M. Baldin, ed.), Joint Inst. Nucl. Res., Dubna (1969), p. 13.Google Scholar
  9. 9.
    L. F. Abbot, Nucl. Phys. B, 185, 189 (1982).CrossRefADSGoogle Scholar
  10. 10.
    I. Jack and H. Osborn, Nucl. Phys. B, 207, 474 (1982).CrossRefADSGoogle Scholar
  11. 11.
    J. P. Bornsen and A. E. M. van de Ven, Nucl. Phys. B, 657, 257 (2003).CrossRefADSGoogle Scholar
  12. 12.
    A. M. Polyakov, Gauge Fields and Strings (Contemporary Concepts in Physics, Vol. 3), Harwood, Chur, Switzerland (1987).Google Scholar
  13. 13.
    L. D. Faddeev and A. Niemi, Phys. Lett. B, 525, 195 (2002).zbMATHMathSciNetCrossRefADSGoogle Scholar
  14. 14.
    L. D. Faddeev and T. A. Bolokhov, Theor. Math. Phys., 139, 679 (2004).MathSciNetCrossRefGoogle Scholar
  15. 15.
    F. V. Gubarev, L. Stodolsky, and V. I. Zakharov, Phys. Rev. Lett., 86, 2220 (2001); K. I. Kondo, Phys. Lett. B, 514, 335 (2001); H. Verschelde, K. Knecht, K. Van Acoleyen, and M. Vanderkelen, Phys. Lett. B, 516, 307 (2001); hep-th/0105018 (2001).CrossRefADSGoogle Scholar
  16. 16.
    G. K. Savvidy, Phys. Lett. B, 71, 133 (1977).CrossRefADSGoogle Scholar

Copyright information

© Springer Science+Business Media, Inc. 2006

Authors and Affiliations

  • L. D. Faddeev
    • 1
  1. 1.St. Petersburg Department of the Steklov Institute of MathematicsRASSt. PetersburgRussia

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