This is a preview of subscription content, log in via an institution.
Preview
Unable to display preview. Download preview PDF.
References
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.
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.
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.
M. SCHILDER, Trans. Amer. Math. Soc., 125, 63–85 (1965).
B. SIMON, ‘Functional Integration and Quantum Physics', (Academic Press, New York 1979).
M.D. DONSKER and S.R.S. VARADHAN, Phys. Rep. 77, 3, 235–37 (1981) and references cited therein.
R.S. ELLIS and J.R. ROSEN, Bull. Amer. Math. Soc., 3, 1, 705–9 (1980).
R.S. ELLIS and J.R. ROSEN, ‘Asymptotic analysis of Gaussian integrals, I: Isolated minimal points', to appear in Trans. Amer. Math. Soc.
R.S. ELLIS and J.R. ROSEN, Commun. Math. Phys. 82, 153–81 (1981).
C. DeWitt-Morette, Ann. Phys. (N.Y.) 97, 367–99 (1976).
M. MIZRAHI, J. Math. Phys. 20, 844–55, (1979).
S. ALBEVERIO and R. HOEGH-KROHN, Inv. Math. 40, 59–106 (1977).
S. ALBEVERIO, P. BLANCHARD and R. HOEGH-KROHN,'The Trace formula for the Schrödinger operators', Preprint Bielefeld 1980.
C. BENDER and T.T. WU, Phys. Rev. 184, 1231–60 (1969).
C. BENDER and T.T. WU, Phys. Rev. Lett. 27, 7, 461–5 (1971).
C. BENDER and T.T. WU, Phys. Rev. D7, 6, 1620–36 (1973).
L.N. LIPATOV, J. E. T. P. Lett. 25, 2, 104–7 (1977).
E. BREZIN et al, Phys. Rev. D15, 6, 1544–57, 1558-64 (1977).
See Ref. 3, Theorem 18.3 and Chapter 18 in general.
E. HARREL and B. SIMON, Duke Math. J. 47, 845–902 (1980).
See Ref. 1(b) and 1(c).
K. ITO and H.P. MCKEAN, ‘Diffusion Processes and their sample paths', (SpringerVerlag, Berlin, New York 1965).
D. WILLIAMS, ‘Diffusions,Markov Processes and martingales Vol. 1: Foundations', (Wiley 1979).
N.I. AKHIEZER, ‘The Calculus of Variations', (Blaisdell, New York, London 1962). See Chapter 4.
H.H. KUO, Lecture Notes in Mathematics 463, (Springer-Verlag, Berlin, Heidelberg, New York 1975). See page 113.
See Ref 1(a).
A. TRUMAN, ‘The polygonal path formulation of the Feynman Path integral', Lecture Notes in Physics 106, 73–102 (1979).
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.
J.C. COLLINS and D.C. SOPER, Ann. Phys. 112, 209–34 (1978).
G. AUBERSON et al, Il Nuovo Cimento 48A, 1–23 (1978).
V. FIGEROU, Commun. Math. Phys. 79, 401–33 (1981).
N. BOGOLIUBOV and S. TYABLIKOV (1949) ‘N. Bogoliubov's collected papers', (Moscow 1972).
L.D. FADEEV and V.N. POPOV, Phys. Lett 25B, 29–30 (1969)
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.
T. SPENCER, Commun. Math. Phys. 74, 273–80 (1980).
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1982 Springer-Verlag
About this paper
Cite this paper
Davies, I., Truman, A. (1982). Laplace expansions of conditional wiener integrals and applications to quantum physics. In: Albeverio, S., Combe, P., Sirugue-Collin, M. (eds) Stochastic Processes in Quantum Theory and Statistical Physics. Lecture Notes in Physics, vol 173. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-11956-6_109
Download citation
DOI: https://doi.org/10.1007/3-540-11956-6_109
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-11956-2
Online ISBN: 978-3-540-39546-1
eBook Packages: Springer Book Archive