zbMATH — the first resource for mathematics

From the Peierls bracket to the Feynman functional integral. (English) Zbl 1078.81026
The paper consists of two parts written by the first and the second author, respectively. In the first part the functional integration is defined via the Peierls bracket and Schwinger’s variational principle. In the second part the basic properties of functional integration, used in the definition and evaluation of Feynman functional integrals, are presented. The authors say that this is the first contact point between their contributions to functional integration.

81Q30 Feynman integrals and graphs; applications of algebraic topology and algebraic geometry
28C05 Integration theory via linear functionals (Radon measures, Daniell integrals, etc.), representing set functions and measures
46T12 Measure (Gaussian, cylindrical, etc.) and integrals (Feynman, path, Fresnel, etc.) on manifolds
Full Text: DOI
[1] Dirac, P.A.M., Europhysics news, 8, 4, (1977)
[2] DeWitt, B., The global approach to quantum field theory (with corrections), (2004), Oxford University Press Oxford, See also, B. Dewitt, The Peierls Bracket in: C. DeWitt-Morette and J.-B. Zuber (Eds.), Quantum Field Theory: perspective and Prospective, Kluwer Acad. Pub. Dordrech NATO ASI C 530, 1999, pp.111-136
[3] DeWitt-Morette, C.; DeWitt-Morette, C., Commun. math. phys., Commun. math. phys., 37, 63-81, (1974)
[4] Cartier, P.; DeWitt-Morette, C., J. math. phys., 36, 2237-2313, (1995)
[5] J. LaChapelle, Ann. Phys., to appear. Available from: <math-ph 0405031>
[6] Voronov, T., Sov. sci. rev. C. math. phys., 9, 1-138, (1992)
[7] Dirac, P.A.M., The principles of quantum mechanics, (1947), Oxford University Press Oxford, pp. 127-130 · Zbl 0030.04801
[8] Malliavin, P., Stochastic analysis, (1997), Springer-Verlag Berlin · Zbl 0878.60001
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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.