Continuous Representations and Path Integrals, Revisited

  • John R. Klauder
Part of the NATO Advanced Study Institutes Series book series (NSSB, volume 34)


The relation of classical and quantum theories, and the use of semi-classical approximations in quantum problems are topics that pervade all branches of physics. Continuous representations, which are generalizations of coherent states, are ideally suited for the formulation of quantum theory, especially for phase-space, and related, formulations. In addition, it is particularly natural to formulate the path integral in terms of continuous representations. Examples and applications of this approach are presented.


Coherent State Classical Action Continuous Representation Path Integral Extremal Solution 
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  1. 1.
    H. Weyl, The Theory of Groups and Quantum Mechanics (Dover, New York, 1931) §l4;MATHGoogle Scholar
  2. 1a.
    E. Wigner, Phys. Rev. 40, 794 (1932);CrossRefGoogle Scholar
  3. 1b.
    J. E. Moyal, Proc. Cambr. Phil. Soc. 45, 99 (1949).MathSciNetADSCrossRefMATHGoogle Scholar
  4. 2.
    J. R. Klauder, Ann. of Physics 11, 123 (1960).MathSciNetADSCrossRefMATHGoogle Scholar
  5. 3.
    J. R. Klauder, J. Math. Phys. 4 1055, 1058 (1963);MathSciNetADSCrossRefGoogle Scholar
  6. 3a.
    J. R. Klauder, J. Math. Phys. 5, 177 (1964).MathSciNetADSCrossRefMATHGoogle Scholar
  7. 3b.
    In addition see J. McKenna and J. R. Klauder, J. Math. Phys. 5, 878 (1964).MathSciNetADSCrossRefMATHGoogle Scholar
  8. 4.
    See, e.g., P. M. Cohn, Lie Groups (Cambridge University Press, London, 196l), p. 110.Google Scholar
  9. 5.
    J. R. Klauder and E. C. G. Sudarshan, Fundamentals of Quantum Optics (Benjamin, New York, 1968), Chap. 7.Google Scholar
  10. 6.
    See, e.g., E. W. Aslaksen and J. R. Klauder, J. Math. Phys. 10, 2267 (1969);MathSciNetADSCrossRefMATHGoogle Scholar
  11. 6a.
    A. O. Barut and L. Girardello, Commun. Math. Phys. 21, 41 (l97l);MathSciNetCrossRefGoogle Scholar
  12. 6b.
    A. M. Perelomov, Commun. Math. Phys. 26, 222 (1972);MathSciNetADSCrossRefMATHGoogle Scholar
  13. 6c.
    F. A. Berezin, Commun. Math. Phys. 40, 153 (1975).MathSciNetADSCrossRefMATHGoogle Scholar
  14. 7.
    J. R. Klauder, J. Math. Phys. 8, 2392 (1967).ADSCrossRefGoogle Scholar
  15. 8.
    See, e.g., H. B. Callen, Thermodynamics (Wiley, New York, 1961), p. 24.Google Scholar
  16. 9.
    R. P. Feynman and A. R. Hibbs, Quantum Mechanic and Path Integrals (McGraw-Hill, New York, 1965).Google Scholar
  17. 10.
    See, e.g., K. Itô, Proc. Imperial Acad., Tokyo 20, 519 (1944);CrossRefMATHGoogle Scholar
  18. 10a.
    H. P. McKean Jr., Stochastic Integrals (Academic Press, New York, 1969);MATHGoogle Scholar
  19. 10b.
    R. L. Stratonovich, Conditional Markov Processes and Their Application to Optimal Control (Elsevier, New York, 1968);MATHGoogle Scholar
  20. 11c.
    E. J. McShane, Stochastic Calculus and Stochastic Models (Academic Press, New York, 1974).MATHGoogle Scholar
  21. 11.
    See, e.g., P. M. Morse and H. Feshbach, Methods of Theoretical Physics (McGraw-Hill, New York, 1953), Part I, p. 437.MATHGoogle Scholar
  22. 12.
    See, e.g., W. H. Miller, J. Chem. Phys. 53., 1949 (1970), Appendix A.MathSciNetADSCrossRefGoogle Scholar
  23. 13.
    T. Hida, Theory of Prob. Appl. (Moscow) 15, 119 (1970).MATHGoogle Scholar
  24. 14.
    L. D. Faddeev, in Les Houches 1975, Proceedings, Methods in Field Theory, Edited by R. Balian and J. Zinn-Justin (North Holland, Amsterdam, 1970), p. 1.Google Scholar

Copyright information

© Springer Science+Business Media New York 1978

Authors and Affiliations

  • John R. Klauder
    • 1
  1. 1.Bell LaboratoriesMurray HillUSA

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