The Group of Paths in Gravitation and Gauge Theory

  • M. B. Mensky


In 1962 Stanley Mandelstam proposed a new formalism for electrodynamics and gravitation1 with wave functions (fields) depending on paths rather than spacetime points. In 1968 he extended this path-dependent formalism to the gauge theories.2 In the last decade this approach, whose advantage is complete gauge invariance, has been considerably developed in different directions. Wu and Yang showed3 that so-called nonintegrable phase factors arising from the path-dependent approach, represent an electro-magnetic or gauge field more adequately than the field strength does. Many other authors4,5,6 have exploited the path-dependent or contour formalism in the gauge theory. Some new ideas (for example concerning phases of gauge fields and confinement of quarks) were connected essentially with the contour formalism.5 But application of the path-dependent approach to gravitation was almost never discussed in literature.


Gauge Theory Minkowski Space Gauge Field Lorentz Group Curve Spacetime 
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.
    S. Mandelstam, Ann. Phys.19, 1; 25 (1962).MathSciNetADSzbMATHCrossRefGoogle Scholar
  2. 2.
    S. Mandelstam, Phys. Rev.175, 1580 (1968).ADSCrossRefGoogle Scholar
  3. 3.
    T.T. Wu, C.N. Yang, Phys. Rev.D 12, 3845 (1975).MathSciNetADSGoogle Scholar
  4. 4.
    C.N. Yang, Phys. Rev. Lett.33, 445 (1974).MathSciNetADSCrossRefGoogle Scholar
  5. 5.
    K.G. Wilson, Phys. Rev.D 10, 2445 (1974).ADSGoogle Scholar
  6. G. ’t Hooft, Nucl. Phys.B 138, 1 (1978).ADSCrossRefGoogle Scholar
  7. S. Mandelstam, Phys. Rev.D 19, 2391 (1979).ADSGoogle Scholar
  8. 6.
    Y. Nambu. Phys. Lett.B80, 372 (1979)ADSGoogle Scholar
  9. J. Glimm, A. Jaffe, Nucl. Phys.B149, 49 (1979)MathSciNetADSCrossRefGoogle Scholar
  10. A.M. Polyakov, Phys. Lett.B82, 247 (1979)ADSGoogle Scholar
  11. Yu. M. Makaenko, A.A. Migdal, Yadernaya Fizika32, 838 (1980)Google Scholar
  12. I. Ya. Aref’eva, Teor. Mat. Fiz.43, 111 (1980)MathSciNetzbMATHGoogle Scholar
  13. 7.
    M.B. Mensky, Proc. Intern. Sem. on Funct. Math. in Quant. Field Theory and Statistics (Moscow, 1971), prepr. PIAN, N 140, Moscow, 1971, p.29.Google Scholar
  14. M.B. Menskii, Theor. Math. Phys.18(2, 136 (1974).MathSciNetCrossRefGoogle Scholar
  15. 8.
    M. Suveges, Acta Phys. Acad. Sci. Hung.20, 41; 51; 274 (1966).CrossRefGoogle Scholar
  16. M. Süveges, ibid.27, 261 (1969).Google Scholar
  17. 9.
    M.B. Mensky, inGravitation: Problems and Prospects, a memorial volume to A.Z. Petrov, Kiev, Naukova Dumka, 1972, p. 157.Google Scholar
  18. 10.
    M.B. Mensky, Proc. 8th Intern. Conf. on Gen. Relat. and Grav. (Waterloo, 1977), Waterloo, 1977, p.251.Google Scholar
  19. M.B. Mensky, Lett. Math. Phys.2, 175 (1978).MathSciNetADSCrossRefGoogle Scholar
  20. 11.
    M.B. Mensky, Lett. Math. Phys.3, 513 (1979).MathSciNetADSCrossRefGoogle Scholar
  21. M.B. Mensky, inGroup Theoretical Methods in Physics(Proc. Intern. Sem., Zvenigorod, 1979), Moscow, Nauka, 1980, v. II, p. 191.Google Scholar
  22. 12.
    M.B. Mensky, Commun. Math. Phys.47, 97,(1976).MathSciNetADSzbMATHCrossRefGoogle Scholar
  23. M.B. Mensky,Method of Induced Representations: Space-Time and Conception of Particles, Moscow, Nauka, 1976 (in Russian).Google Scholar
  24. 13.
    Y. Aharonov, D. Bohm, Phys. Rev.115, 485 (1959).MathSciNetADSzbMATHCrossRefGoogle Scholar
  25. 14.
    C.J. Isham, Proc. R. Soc. Land.A 362, 383 (1978).MathSciNetADSGoogle Scholar
  26. S.J. Avis, C.J. Isham, Proc. R. Soc. Lond.A 363, 581 (1978).MathSciNetADSGoogle Scholar
  27. J.S. Dowker, R. Banach, J. Phys.A 11, 2255 (1978)MathSciNetADSGoogle Scholar
  28. 15.
    B.S. DeWitt, C.F. Hart, C.J. Isham, PhysicaA 96, 197 (1979).MathSciNetADSGoogle Scholar
  29. 16.
    P.A.M. Dirac, in Problems of Theoretical Physics, a memorial volume to I.E. Tamm, Moscow, Nauka, 1972, p. 45.Google Scholar

Copyright information

© Plenum Press, New York 1984

Authors and Affiliations

  • M. B. Mensky
    • 1
  1. 1.USSR State Committee for StandardsMoscowRussia

Personalised recommendations