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Feynman’s path integral. Definition without limiting procedure. (English) Zbl 0239.46041


MSC:

46G99 Measures, integration, derivative, holomorphy (all involving infinite-dimensional spaces)
46N99 Miscellaneous applications of functional analysis
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[1] Feynman, R. P., Hibbs, A. R.: Quantum mechanics and path integrals. New York: McGraw Hill Book Comp. 1965. · Zbl 0176.54902
[2] Laidlaw, M. G. G., DeWitt, C. Morette: Phys. Rev. D3, 1375–1378 (1971). – Laidlaw, M. G. G.: Ph. D. Thesis, University of North Carolina, 1971. · doi:10.1103/PhysRevD.3.1375
[3] DeWitt, C. Morette: Ann. Inst. H. Poincaré11, 153–206 (1969). A misprint occurs on p. 162 in the line following “développonsS en série de Taylor{”; it should read:}
[4] Bourbaki, N.: Eléments de mathematiques. Chapter IX, Volume VI – also referred to as Fasicule 35 or No. 1343 of the Actualités Scientifiques et Industrielles – Paris, Hermann 1969. See also Friedrichs, K. O., Shapiro, H. N.et al.: Integration of functionals. Seminar Notes of the Institute of Mathematical Sciences of New York University 1957.
[5] Choquet, G.: Mesures coniques, affines et cylindriques. Conferenza, Istituto di Alta Matematica, 1968.
[6] Nelson, E.: J. Math. Phys.5, 332–343 (1964). · Zbl 0133.22905 · doi:10.1063/1.1704124
[7] Cameron, R. H.: J. Math. Phys.39, 126–140 (1960).
[8] Schwartz, L.: Théorie des distributions. Paris: Hermann 1966.
[9] Rudin, W.: Fourier analysis on groups. New York: Interscience Publ. 1962. · Zbl 0107.09603
[10] Faddeef, L. D., Popov, V. N.: Phys. Letters25 B, 29 (1967). See also Ref. [3], pp. 196, 200–202.
[11] Dyson, F. J.: Missed opportunities. 1972. J. W. Gibbs lecture; Bull. Am. Math. Soc. to appear in 1972.
[12] Gel’fand, I. M., Yaglom, A. M.: J. Math. Phys.1, 48–69 (1960) (translated from Uspekhi Mat. Nauk11, 77, 1956.). · Zbl 0092.45105 · doi:10.1063/1.1703636
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