Functional Integration A Multipurpose Tool

Cécile DeWitt-Morette

Recherche Coopérative sur Programme n°25 (1993)

  • Volume: 44, page 1-24

How to cite


DeWitt-Morette, Cécile. "Functional Integration A Multipurpose Tool." Recherche Coopérative sur Programme n°25 44 (1993): 1-24. <>.

author = {DeWitt-Morette, Cécile},
journal = {Recherche Coopérative sur Programme n°25},
language = {eng},
pages = {1-24},
publisher = {Institut de Recherche Mathématique Avancée - Université Louis Pasteur},
title = {Functional Integration A Multipurpose Tool},
url = {},
volume = {44},
year = {1993},

AU - DeWitt-Morette, Cécile
TI - Functional Integration A Multipurpose Tool
JO - Recherche Coopérative sur Programme n°25
PY - 1993
PB - Institut de Recherche Mathématique Avancée - Université Louis Pasteur
VL - 44
SP - 1
EP - 24
LA - eng
UR -
ER -


  1. [a] Cécile Morette DeWitt (1972) "Feynman's Path Integral; Definition Without Limiting Procedure", Commun. Math. Phys.28, 47-67. Zbl0239.46041MR309456
  2. [b] Cécile DeWitt-Morette (1974) "Feynman Path Integrals; I. Linear and Affine Techniques; II. The Feynman-Green Function", Commun. Math. Phys.37, 63-81. Zbl0287.28006MR353903
  3. [c] Cécile DeWitt-Morette (1976) "The Semi-Classical Expansion", Annals of Physics97, 367-399. Zbl0328.46075MR416368
  4. [d] Maurice M. Mizrahi (1979) "The semiclassical expansion of the anharmonic-oscillator propagator" J. Math. Phys. 20, 844-855. Zbl0417.70009MR531287
  5. [e] C. DeWitt-Morette, A. Maheshwari and B. Nelson (1979) "Path Integration in Non relativistic Quantum Mechanics", Physics Reports50, 266-372. MR525283
  6. [f] Cécile DeWitt-Morette and Tian-Rong Zhang (1983) "Path Integrals and Conservation Laws", Phys. Rev. D28, 2503-2516. MR726167
  7. [g] Cécile DeWitt-Morette and Tian-Rong Zhang (1983) "Feynman-Kac formula in phase space with application to coherent-state transitions", Phys. Rev. D28, 2517-2525. MR726168
  8. [h] Cécile DeWitt-Morette, Bruce Nelson and Tian-Rong Zhang (1983) "The Caustic Problem in Quantum Mechanics with Application to Scattering Theory", Phys. Rev. D28, 2526-2546. MR726169
  9. [i] Cécile DeWitt-Morette and Bruce Nelson (1984) "Glories - and other degenerate critical points of the action", Phys. Rev. D29, 1663-1668. 
  10. [j] P. Anninos, C. DeWitt-Morette, R. Matzner, P. Yioutas and T.-R. Zhang (1992). Orbiting cross-sections, application to black hole scattering. Armadillo preprint. 
  11. [k] Cécile DeWitt-Morette (1984) "Feynman path integrals. From the Prodistribution Definition to the Calculation of Glory Scattering", in Stochastic Methods and Computer Techniques in Quantum Dynamics, ed. H. Mitter and L. Pittner, Acta Physica Austriaca Supp.26, 101-170. Reviewed in Zentralblatt für Mathematik1985. Zbl0549.60051MR787074
  12. [l] Cécile DeWitt-Morette (1990) "Quantum Mechanics in Curved Spacetimes ; Stochastic Processes on Frame Bundles" in Quantum Mechanics in Curved Space-Time. Ed. by J. Audretsch and V. de Sabbata (Plenum Press, New-York). Zbl0729.53069MR1145039
  13. See reference l.d. 
  14. Michael G.G. Laidlaw and Cécile Morette DeWitt (1971) "Feynman Functional Integrals for Systems of Indistinguishable Particles" Phys. Rev. D3, 1375-1378. 
  15. Computed in l.i, using results developed in l.f, l.g, l.h ; summarized in l.k. 
  16. [a] Richard P. Feynman (1942) "The principle of Least Action in Quantum Mechanics" (Princeton University Ph. D. Dissertation) Available from University Microfilms Inc. P.O. Box 1307, Ann Arbor, MI 48106. Tel 1-800-521 0600. 
  17. [b] Sergio A. Albeverio and Raphael J. Høegh-Krohn (1976) Mathematical Theory of Feynman Path Integrals (Lecture Notes in Mathematics # 523, Springer-Verlag, Berlin) Zbl0337.28009MR2453734
  18. S. Albeverio, A. Boutet de Monvel-Berthier, and Z. Brzezniak (1992) "The trace formula for Schrödinger operators from infinite dimensional oscillatory integrals". Bibos preprint and references therein (submitted to Crelle's Journal). Zbl0866.58020MR1419888
  19. [c] R.H. Cameron and D.A. Storvick (1983) "A simple definition of the Feynman integral, with applications" Memoirs of the American Mathematical Society #288 (Providence, Rhode Island) and references therein. Zbl0527.28015
  20. The construction called here the "Cartier Bridge" will be published in a Note aux Compte-Rendus de l'Académie des Sciences by P. Cartier and C. DeWitt-Morette. In the years to come the authors will write a book on functional integration and test the proposed axiomatic on many problems of physical interest. 
  21. [a] General T. Hida, H.-H. Kuo, J. Potthoff, L. Streit. "White Noise - An Infinite Dimensional Calculus" monograph to appear. Zbl0771.60048MR1244577
  22. H.-H. Kuo. (1991) "Lectures on White Noise Analysis", in Proc. Preseminar Intl. Conf. on Gaussian Random Fields, edited by T. Hida and K. Saito, Nagoya. Zbl0783.60064MR1187744
  23. [b] Characterization Theorem J. Potthoff, and L. Streit. (1991) "A characterization of Hida distributions", J. Funct. Analysis101, 212. Zbl0826.46035MR1132316
  24. [c] Feynman Integrals T. Hida, and L. Streit. (1983) "Generalized Brownian functionals and the Feynman integral". Stoch. Proc. Appl.16, 55-69. Zbl0575.60039MR723643
  25. M. de Faria. (1991) "White Noise Analysis and the Feynman integral". Universidade da Madeira preprint UMa-Mat 4/91, to appear in Proc. III. Intl. Conf. Stoch. Proc, Physics, and Geometry, Locarno. 
  26. M. de Faria, J. Potthoff, L. Streit. (1991). "The Feynman integrand as a Hida distribution" J. Math. Phys.32, 2123 (1991). Zbl0754.46050MR1123604
  27. D.C. Khandekar, L. Streit. (1992) "Constructing the Feynman integrand" Ann. Physik1, 49. MR1161912
  28. L. Streit. (1992) "The Feynman Integral. Recent results" Universidade da Madeira Preprint UMa-Mat 10/92. MR1340441
  29. K. Bleuler (1950) Helvetica Phys. Acta23, 567. Zbl0040.42404MR38883
  30. S.N. Gupta (1950) Proc. Phys. Soc. A63, 681. MR36166
  31. K. Bleuler (1950) Helvetica Phys. Acta23, 567. Zbl0040.42404MR38883
  32. S.N. Gupta (1950) Proc. Phys. Soc. A63, 681. MR36166
  33. Paul Krée (1988) "La Théorie des distributions en dimension quelconque et l'Intégration stochastique" dans Stochastic Analysis and Related Topics Eds H. Korezlioglu and A.S. Ustunel, pp. 170-233 (Lecture Notes in Mathematics # 1316, Springer-Verlag). Zbl0648.60063MR953796
  34. P. Malliavin (1993) Stochastic Analysis (Grundlehren der Mathematik, Springer-Verlag, Berlin). Zbl0878.60001MR1450093
  35. P.A. Meyer (1986-1987) "Eléments de probabilités quantiques", in Séminaire des Probabilités XX (Lecture Notes in Mathematics #1247) Eds J. Azéma, P.A. Meyer, et M. Yor (Springer-Verlag, Berlin). Zbl0633.60074
  36. L.S. Schulman (1968) "A Path Integral for Spin" Phys. Rev.176, 1558-1569. Zbl1020.81669MR237149

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