Functional Integration A Multipurpose Tool
Les rencontres physiciens-mathématiciens de Strasbourg -RCP25, Tome 44 (1993), Exposé no. 1, 24 p.
@article{RCP25_1993__44__1_0,
     author = {DeWitt-Morette, C\'ecile},
     title = {Functional {Integration} {A} {Multipurpose} {Tool}},
     journal = {Les rencontres physiciens-math\'ematiciens de Strasbourg -RCP25},
     note = {talk:1},
     publisher = {Institut de Recherche Math\'ematique Avanc\'ee - Universit\'e Louis Pasteur},
     volume = {44},
     year = {1993},
     language = {en},
     url = {http://archive.numdam.org/item/RCP25_1993__44__1_0/}
}
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DeWitt-Morette, Cécile. Functional Integration A Multipurpose Tool. Les rencontres physiciens-mathématiciens de Strasbourg -RCP25, Tome 44 (1993), Exposé no. 1, 24 p. http://archive.numdam.org/item/RCP25_1993__44__1_0/

[a] Cécile Morette Dewitt (1972) "Feynman's Path Integral; Definition Without Limiting Procedure", Commun. Math. Phys. 28, 47-67. | MR 309456 | Zbl 0239.46041

[b] Cécile Dewitt-Morette (1974) "Feynman Path Integrals; I. Linear and Affine Techniques; II. The Feynman-Green Function", Commun. Math. Phys. 37, 63-81. | MR 353903 | Zbl 0287.28006

[c] Cécile Dewitt-Morette (1976) "The Semi-Classical Expansion", Annals of Physics 97, 367-399. | MR 416368 | Zbl 0328.46075

[d] Maurice M. Mizrahi (1979) "The semiclassical expansion of the anharmonic-oscillator propagator" J. Math. Phys. 20, 844-855. | MR 531287 | Zbl 0417.70009

[e] C. Dewitt-Morette, A. Maheshwari and B. Nelson (1979) "Path Integration in Non relativistic Quantum Mechanics", Physics Reports 50, 266-372. | MR 525283

[f] Cécile Dewitt-Morette and Tian-Rong Zhang (1983) "Path Integrals and Conservation Laws", Phys. Rev. D28, 2503-2516. | MR 726167

[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. | MR 726168

[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. | MR 726169

[i] Cécile Dewitt-Morette and Bruce Nelson (1984) "Glories - and other degenerate critical points of the action", Phys. Rev. D29, 1663-1668.

[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.

[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 Mathematik 1985. | MR 787074 | Zbl 0549.60051

[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). | MR 1145039 | Zbl 0729.53069

See reference l.d.

Michael G.G. Laidlaw and Cécile Morette Dewitt (1971) "Feynman Functional Integrals for Systems of Indistinguishable Particles" Phys. Rev. D3, 1375-1378.

Computed in l.i, using results developed in l.f, l.g, l.h ; summarized in l.k.

[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.

[b] Sergio A. Albeverio and Raphael J. Høegh-Krohn (1976) Mathematical Theory of Feynman Path Integrals (Lecture Notes in Mathematics # 523, Springer-Verlag, Berlin) | MR 2453734 | Zbl 0337.28009

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). | MR 1419888 | Zbl 0866.58020

[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. | Zbl 0527.28015

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.

[a] General T. Hida, H.-H. Kuo, J. Potthoff, L. Streit. "White Noise - An Infinite Dimensional Calculus" monograph to appear. | MR 1244577 | Zbl 0771.60048

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. | MR 1187744 | Zbl 0783.60064

[b] Characterization Theorem J. Potthoff, and L. Streit. (1991) "A characterization of Hida distributions", J. Funct. Analysis 101, 212. | MR 1132316 | Zbl 0826.46035

[c] Feynman Integrals T. Hida, and L. Streit. (1983) "Generalized Brownian functionals and the Feynman integral". Stoch. Proc. Appl. 16, 55-69. | MR 723643 | Zbl 0575.60039

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.

M. De Faria, J. Potthoff, L. Streit. (1991). "The Feynman integrand as a Hida distribution" J. Math. Phys. 32, 2123 (1991). | MR 1123604 | Zbl 0754.46050

D.C. Khandekar, L. Streit. (1992) "Constructing the Feynman integrand" Ann. Physik 1, 49. | MR 1161912

L. Streit. (1992) "The Feynman Integral. Recent results" Universidade da Madeira Preprint UMa-Mat 10/92. | MR 1340441

K. Bleuler (1950) Helvetica Phys. Acta 23, 567. | MR 38883 | Zbl 0040.42404

S.N. Gupta (1950) Proc. Phys. Soc. A63, 681. | MR 36166

K. Bleuler (1950) Helvetica Phys. Acta 23, 567. | MR 38883 | Zbl 0040.42404

S.N. Gupta (1950) Proc. Phys. Soc. A63, 681. | MR 36166

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). | MR 953796 | Zbl 0648.60063

P. Malliavin (1993) Stochastic Analysis (Grundlehren der Mathematik, Springer-Verlag, Berlin). | MR 1450093 | Zbl 0878.60001

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). | Numdam | Zbl 0633.60074

L.S. Schulman (1968) "A Path Integral for Spin" Phys. Rev. 176, 1558-1569. | MR 237149 | Zbl 1020.81669