Analytic and sequential Feynman integrals on abstract Wiener and Hilbert spaces, and a Cameron-Martin formula

G. Kallianpur; D. Kannan; R. L. Karandikar

Annales de l'I.H.P. Probabilités et statistiques (1985)

  • Volume: 21, Issue: 4, page 323-361
  • ISSN: 0246-0203

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Kallianpur, G., Kannan, D., and Karandikar, R. L.. "Analytic and sequential Feynman integrals on abstract Wiener and Hilbert spaces, and a Cameron-Martin formula." Annales de l'I.H.P. Probabilités et statistiques 21.4 (1985): 323-361. <http://eudml.org/doc/77262>.

@article{Kallianpur1985,
author = {Kallianpur, G., Kannan, D., Karandikar, R. L.},
journal = {Annales de l'I.H.P. Probabilités et statistiques},
keywords = {abstract Wiener space; Cameron-Martin formula; analytic Feynman and sequential Feynman integrals; Maslov index},
language = {eng},
number = {4},
pages = {323-361},
publisher = {Gauthier-Villars},
title = {Analytic and sequential Feynman integrals on abstract Wiener and Hilbert spaces, and a Cameron-Martin formula},
url = {http://eudml.org/doc/77262},
volume = {21},
year = {1985},
}

TY - JOUR
AU - Kallianpur, G.
AU - Kannan, D.
AU - Karandikar, R. L.
TI - Analytic and sequential Feynman integrals on abstract Wiener and Hilbert spaces, and a Cameron-Martin formula
JO - Annales de l'I.H.P. Probabilités et statistiques
PY - 1985
PB - Gauthier-Villars
VL - 21
IS - 4
SP - 323
EP - 361
LA - eng
KW - abstract Wiener space; Cameron-Martin formula; analytic Feynman and sequential Feynman integrals; Maslov index
UR - http://eudml.org/doc/77262
ER -

References

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  1. [1] S.A. Albeverio and R.J. Høegh-Krohn, Mathematical Theory of Feynman Path Integrals. Lecture Notes in Mathematics, n° 523. Springer-Verlag, Berlin, 1976. Zbl0337.28009MR495901
  2. [2] R.H. Cameron D.A. Storvick, Some Banach algebras of analytic Feynman integrable functionals. Analytic Functions, Kozubnik, 1979. Lecture Notes in Mathematics, n° 798. Springer-Verlag, Berlin, 1980, p. 18-67. Zbl0439.28007MR577446
  3. [3] R.H. Cameron and D.A. Storvick, A simple definition of the Feynman integral with applications. Memoirs of the American Mathematical Society, n° 288, 1983. Zbl0527.28015
  4. [4] Ph. Combe, R. Rodriguez, G. Rideau and M. Sirugue-Collin, On the cylindrical approximation of the Feynman path integral. Reports on Mathematical Physics, t. 13, 1978, p. 279-294. Zbl0421.28014
  5. [5 a] K.D. Elworthy and A. Truman, A Cameron-Martin formula for Feynman integrals. (The origin of Maslov indices). VI International Conference on Mathematical Physics, Berlin, August 1981. 
  6. [5 b] K.D. Elworthy and A. Truman, Feynman maps, Cameron-Martin formulas and anharmonic oscillators, Ann. Inst. Henri Poincaré, 1984. Zbl0578.28013
  7. [6] R.P. Feynman, Space time approach to non-relativistic quantum mechanics. Rev. Mod. Phys., t. 20, 1948, p. 367-387. MR26940
  8. [7] R.P. Feynman and A.R. Hibbs, Quantum Mechanics and Path Integrals. McGraw-Hill, New York, 1965. Zbl0176.54902
  9. [8] L. Gross, Measurable functions on Hilbert space, Transactions of the Amer. Math. Soc., t. 105, 1962, p. 372-390. Zbl0178.50001MR147606
  10. [9] K. Ito, Generalized uniform complex measures in the Hibertian metric space with their application to the Feynman integral. Proc. Fifth Berkeley symposium on Mathematical Statistics and Probability, 1967, II, Part 1, p. 145-161. MR216528
  11. [10] G.W. Johnson, The equivalence of two approaches to Feynman integral. J. Math. Phys., t. 23, 1982, p. 2090-2096. Zbl0496.60068MR680005
  12. [11] G. Kallianpur and C. Bromley, Generalized Feynman Integrals Using Analytic Continuation in Several Complex Variables. Stochastic Analysis, M. Pinsky, ed., Marcel-Dekker, 1984. Zbl0554.60061MR776983
  13. [12] G. Kallianpur, A Cameron-Martin Formula for Feynman Integrals. Tech. Rept. # 13, Center for Stochastic Processes, Dept. of Statistics, Univ. of North Carolina, Chapel Hill, 1982. Zbl0495.60059
  14. [13] H.H. Kuo, Gaussian Measures in Banach Spaces. Lecture Notes in Mathematics, n° 463, Springer, Berlin, 1975. Zbl0306.28010MR461643
  15. [14] J. Tarski, Feynman type integrals defined in terms of general cylindrical approximations. Feynman Path Integrals, S. Albeverio et al., eds., Lecture Notes in Physics, t. 106, Springer-Verlag, 1979, p. 254-278. MR553089
  16. [15] A. Truman, The polygonal path formulation of the Feynman path integrals. Feynman Path Integrals, S. Albeverio et al., eds., Lecture Notes in Physics, t. 106, Springer-Verlag, 1979, p. 73-102. Zbl0412.28009MR553077
  17. [16] N. Dunford and J.T. Schwartz, Linear Operators. Part II, Interscience Publishers, New York, London, 1963. Zbl0128.34803MR188745

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