Cartier, Pierre; DeWitt-Morette, Cécile Functional integration. (English) Zbl 0974.58011 J. Math. Phys. 41, No. 6, 4154-4187 (2000). Summary: Three approaches to functional integration are compared: Feynman’s definition and the Feynman-Kac formula, Bryce DeWitt’s formalism, and the authors’ axiomatic scheme. They serve to highlight the evolution of functional integration in the second half of the twentieth century. Cited in 6 Documents MSC: 58D30 Applications of manifolds of mappings to the sciences 46F25 Distributions on infinite-dimensional spaces 60H40 White noise theory 81-02 Research exposition (monographs, survey articles) pertaining to quantum theory 81S40 Path integrals in quantum mechanics Keywords:Feynman’s path integral; functional integration; Feynman-Kac formula; Bryce DeWitt’s formalism PDFBibTeX XMLCite \textit{P. Cartier} and \textit{C. DeWitt-Morette}, J. Math. Phys. 41, No. 6, 4154--4187 (2000; Zbl 0974.58011) Full Text: DOI References: [1] Segal I. E., Trans. Am. Math. Soc. 88 pp 12– (1958) · doi:10.1090/S0002-9947-1958-0102759-X [2] DOI: 10.1063/1.881190 · doi:10.1063/1.881190 [3] Dyson F. J., Phys. Rev. 75 pp 486– (1949) · Zbl 0032.23702 · doi:10.1103/PhysRev.75.486 [4] DOI: 10.1103/PhysRev.81.848 · Zbl 0042.45506 · doi:10.1103/PhysRev.81.848 [5] Dyson F. J., Bull. Am. Math. Soc. 78 (5) pp 635– (1972) · Zbl 0271.01005 · doi:10.1090/S0002-9904-1972-12971-9 [6] DOI: 10.1002/sapm1960391126 · Zbl 0096.06901 · doi:10.1002/sapm1960391126 [7] DOI: 10.1103/PhysRevD.3.1375 · doi:10.1103/PhysRevD.3.1375 [8] DOI: 10.1007/BF01217730 · Zbl 0667.57005 · doi:10.1007/BF01217730 [9] DOI: 10.1063/1.530631 · Zbl 0799.58078 · doi:10.1063/1.530631 [10] DOI: 10.1063/1.530631 · Zbl 0799.58078 · doi:10.1063/1.530631 [11] Morette DeWitt C., Commun. Math. Phys. 28 pp 47– (1972) · Zbl 0239.46041 · doi:10.1007/BF02099371 [12] DeWitt-Morette C., Commun. Math. Phys. 37 pp 63– (1973) · Zbl 0287.28006 · doi:10.1007/BF01646034 [13] Krée P., Bull. Soc. Math. France 46 pp 143– (1976) [14] DOI: 10.1016/0370-1573(79)90083-8 · doi:10.1016/0370-1573(79)90083-8 [15] DOI: 10.1063/1.531039 · Zbl 0853.58023 · doi:10.1063/1.531039 [16] DeWitt-Morette C., Acta Phys. Austriaca, Suppl. 26 pp 101– (1984) [17] Brydges D., Commun. Math. Phys. 198 pp 111– (1998) · Zbl 0924.46062 · doi:10.1007/s002200050474 [18] DOI: 10.1103/PhysRev.81.848 · Zbl 0042.45506 · doi:10.1103/PhysRev.81.848 [19] DeWitt-Morette C., Ann. Inst. Henri Poincaré, Sect. A 32 pp 327– (1980) [20] Freed D. S., Commun. Math. Phys. 147 pp 563– (1992) · Zbl 0755.53054 · doi:10.1007/BF02097243 [21] Blau M., J. Math. Phys. 36 pp 2192– (1995) · Zbl 0844.58105 · doi:10.1063/1.531038 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.