Classical Gauge Theories and Their Quantum Role

  • Arthur Jaffe
Part of the NATO Advanced Study Institutes Series book series (NSSB, volume 59)


The classical Euclidean variational equations (δA= 0, where A is the action functional, play two important roles. First, in dimension d ≤ 3 they provide time independent solutions to classical four-dimensional physics. In that way, for example, the Ginzburg-Landau model has proved important in the theory of superconductivity. The second role of Euclidean stationary points of the action is to provide a starting point for classical approximations to quantum fields. We make some remarks on these two topics; for classical gauge theories we restrict attention to the Higgs model.


Classical Solution Flux Tube Vortex Solution Vortex Configuration Finite Action 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    V.L. Ginzburg and L.D. Landau, Zh. Eksp. Theor. Fiz. 20 (1950) 10647Google Scholar
  2. A.A. Abrikosov, J.E.T.P. 5 (1957) 1174 (translation).Google Scholar
  3. 2.
    The results of C.H. Taubes can be found in his Harvard Ph.D. Thesis (1980) as well as in two papers to appear in Comm. Math. Phys.: “Arbitrary n-vortex solutions to the first order Ginzburg-Landau equations” and “Equivalence of first and second order equations for gauge theories.”Google Scholar
  4. 3.
    L. Jacobs and C. Rebbi, Phys. Rev. B19 (1979) 4486.MathSciNetADSGoogle Scholar
  5. 4.
    E. Bogomol’nyi, Sov. J. Nucl. Phys. 24 (1976) 449.MathSciNetGoogle Scholar
  6. 5.
    H. deVega and F. Schnaposnik, Phys. Rev. D14 (1976) 1100.ADSGoogle Scholar
  7. 6.
    E. Weinberg, Phys. Rev. D19 (1979) 3008.ADSGoogle Scholar
  8. 7.
    T. Jonsson, O. McBryan, F. Zivilli, J. Hubbard, Comm. Math. Phys. 68 (1979) 259.MathSciNetADSMATHCrossRefGoogle Scholar
  9. 8.
    G. Woo, J. Math. Phys. 18 (1977) 1264.MathSciNetADSCrossRefGoogle Scholar
  10. W. Garber, S. Ruijsenaars, E. Seiler and D. Burns, Ann. Phys. 119 (1979) 305.MathSciNetADSMATHCrossRefGoogle Scholar
  11. 9.
    R. Flume, Phys. Lett. 76B (1978) 593.MathSciNetGoogle Scholar
  12. 10.
    E. Witten, Phys. Rev. Lett. 38 (1977) 121.ADSCrossRefGoogle Scholar
  13. D. Forcas and N. Manton, Commun. Math. Phys., to appear.Google Scholar
  14. 11.
    J. Glimm and A. Jaffe, 1976 Cargêse Lectures, and References there, as well as their forthcoming book.Google Scholar
  15. 12.
    D. Brydges, J. Fröhlich and E. Seiler, Ann. Phys. 121 (1979) 227, and Comm. Math. Phys. to appear.Google Scholar
  16. 13.
    J. Glimm, A. Jaffe and T. Spencer, Ann. Phys. 101 (1976) 610 and 101 (1976) 631.Google Scholar
  17. 14.
    T. Balaban and K. Gawedski, preprint.Google Scholar

Copyright information

© Plenum Press, New York 1980

Authors and Affiliations

  • Arthur Jaffe
    • 1
  1. 1.Harvard UniversityCambridgeUSA

Personalised recommendations