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Laplace expansions of conditional wiener integrals and applications to quantum physics

  • Ian Davies
  • Aubrey Truman
Conference paper
Part of the Lecture Notes in Physics book series (LNP, volume 173)

Keywords

Anharmonic Oscillator Zeeman Effect Reflection Principle Frechet Derivative Wiener Integral 
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.

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References

  1. [1a]
    I.M. DAVIES and A. TRUMAN, ‘Laplace asymptotic expansions of conditional Wiener integrals and generalised Mehler kernel formulas', accepted for publication by J. Math. Phys.Google Scholar
  2. [1b]
    I.M. DAVIES and A. TRUMAN, ‘On the Laplace asymptotic expansion of conditional Wiener integrals and the Bender-Wu formula for X2N anharmonic oscillator', accepted for publication by J. Math, Phys.Google Scholar
  3. [1c]
    I.M. DAVIES and A. TRUMAN, ‘Laplace asymptotic expansions of conditional Wiener integrals and generalised Mehler formulas for Hamiltonians on ℜn, to be submitted to J. Phys. A.Google Scholar
  4. [2]
    M. SCHILDER, Trans. Amer. Math. Soc., 125, 63–85 (1965).Google Scholar
  5. [3]
    B. SIMON, ‘Functional Integration and Quantum Physics', (Academic Press, New York 1979).Google Scholar
  6. [4]
    M.D. DONSKER and S.R.S. VARADHAN, Phys. Rep. 77, 3, 235–37 (1981) and references cited therein.Google Scholar
  7. [5a]
    R.S. ELLIS and J.R. ROSEN, Bull. Amer. Math. Soc., 3, 1, 705–9 (1980).Google Scholar
  8. [5b]
    R.S. ELLIS and J.R. ROSEN, ‘Asymptotic analysis of Gaussian integrals, I: Isolated minimal points', to appear in Trans. Amer. Math. Soc.Google Scholar
  9. [5c]
    R.S. ELLIS and J.R. ROSEN, Commun. Math. Phys. 82, 153–81 (1981).Google Scholar
  10. [6]
    C. DeWitt-Morette, Ann. Phys. (N.Y.) 97, 367–99 (1976).Google Scholar
  11. [7]
    M. MIZRAHI, J. Math. Phys. 20, 844–55, (1979).Google Scholar
  12. [8a]
    S. ALBEVERIO and R. HOEGH-KROHN, Inv. Math. 40, 59–106 (1977).Google Scholar
  13. [8b]
    S. ALBEVERIO, P. BLANCHARD and R. HOEGH-KROHN,'The Trace formula for the Schrödinger operators', Preprint Bielefeld 1980.Google Scholar
  14. [9a]
    C. BENDER and T.T. WU, Phys. Rev. 184, 1231–60 (1969).Google Scholar
  15. [9b]
    C. BENDER and T.T. WU, Phys. Rev. Lett. 27, 7, 461–5 (1971).Google Scholar
  16. [9c]
    C. BENDER and T.T. WU, Phys. Rev. D7, 6, 1620–36 (1973).Google Scholar
  17. [10]
    L.N. LIPATOV, J. E. T. P. Lett. 25, 2, 104–7 (1977).Google Scholar
  18. [11]
    E. BREZIN et al, Phys. Rev. D15, 6, 1544–57, 1558-64 (1977).Google Scholar
  19. [12a]
    See Ref. 3, Theorem 18.3 and Chapter 18 in general.Google Scholar
  20. [12b]
    E. HARREL and B. SIMON, Duke Math. J. 47, 845–902 (1980).Google Scholar
  21. [13]
    See Ref. 1(b) and 1(c).Google Scholar
  22. [14]
    K. ITO and H.P. MCKEAN, ‘Diffusion Processes and their sample paths', (SpringerVerlag, Berlin, New York 1965).Google Scholar
  23. [15]
    D. WILLIAMS, ‘Diffusions,Markov Processes and martingales Vol. 1: Foundations', (Wiley 1979).Google Scholar
  24. [16]
    N.I. AKHIEZER, ‘The Calculus of Variations', (Blaisdell, New York, London 1962). See Chapter 4.Google Scholar
  25. [17]
    H.H. KUO, Lecture Notes in Mathematics 463, (Springer-Verlag, Berlin, Heidelberg, New York 1975). See page 113.Google Scholar
  26. [18a]
    See Ref 1(a).Google Scholar
  27. [18b]
    A. TRUMAN, ‘The polygonal path formulation of the Feynman Path integral', Lecture Notes in Physics 106, 73–102 (1979).Google Scholar
  28. [19]
    B. SIMON, ‘Large Orders and Summability of Eigenvalue Perturbation Theory: A Mathematical Overview', to appear in Int. J. Quant. Chem., Proceedings of 1981 Sanibel workshop.Google Scholar
  29. [20]
    J.C. COLLINS and D.C. SOPER, Ann. Phys. 112, 209–34 (1978).Google Scholar
  30. [21]
    G. AUBERSON et al, Il Nuovo Cimento 48A, 1–23 (1978).Google Scholar
  31. [22]
    V. FIGEROU, Commun. Math. Phys. 79, 401–33 (1981).Google Scholar
  32. [23a]
    N. BOGOLIUBOV and S. TYABLIKOV (1949) ‘N. Bogoliubov's collected papers', (Moscow 1972).Google Scholar
  33. [23b]
    L.D. FADEEV and V.N. POPOV, Phys. Lett 25B, 29–30 (1969)Google Scholar
  34. [24]
    We have been informed by Barry Simon that the problem of the commutativity of the limits in T and n has been solved by Steven Breen, a former student of T. Spencer.Google Scholar
  35. [25]
    T. SPENCER, Commun. Math. Phys. 74, 273–80 (1980).Google Scholar

Copyright information

© Springer-Verlag 1982

Authors and Affiliations

  • Ian Davies
    • 1
  • Aubrey Truman
    • 1
  1. 1.Mathematics DepartmentHeriot-Watt UniversityCurrie, Edinburgh

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