×

On the quantum Feynman-Kac formula. (English) Zbl 0437.60030


MSC:

60G20 Generalized stochastic processes
60J25 Continuous-time Markov processes on general state spaces
60B15 Probability measures on groups or semigroups, Fourier transforms, factorization
60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
81P20 Stochastic mechanics (including stochastic electrodynamics)
81Q30 Feynman integrals and graphs; applications of algebraic topology and algebraic geometry
PDF BibTeX XML Cite
Full Text: DOI

References:

[1] Accardi L.,Non commutative Markov chains. Proceedings, School in Math. Phys., Camerino 1974.
[2] Accardi L.,Non relativistic quantum mechanics as a non-commutative Markof process. Advances in Math.20 (1976), 329–366. · Zbl 0367.60119
[3] Accardi L.,Problemi matematici della meccanica quantistica. Rendiconti del convegno annuale del G.N.A.F.A., Rimini 1977.
[4] Accardi L.,Local perturbations of conditional expectations. To appear in: J. Math. Anal. Appl. · Zbl 0435.60100
[5] Accardi L.,Markovian cocycles. To appear in: Proceedings of the Royal Irish Academy.
[6] Araki H.,Expansionals in Banach algebras. Ann. Sci. Ecole Norm. Sup.6 (1973), 67–84. · Zbl 0257.46054
[7] Carmona R.,Regularity properties of Schrödinger and Dirichlet semigroups. J. Functional Analysis, to appear. · Zbl 0419.60075
[8] Carmona R.,Pointwise bounds for Schrödinger eigenstates. Comm. Math. Phys.62 (1978), 97–106. · Zbl 0403.47016
[9] Davies E. B.,Generators of dynamical semigroups. Preprint Oxford. · Zbl 0428.47021
[10] Doob J. L.,Stochastic processes. John Wiley and Sons Inc. (1967).
[11] Dynkin E. B.,Markov processes. Springer Verlag (1965). · Zbl 0132.37901
[12] Evans D.
[13] Evans D., Lewis J. T.,Dilations of irreversible evolutions in algebraic quantum theory. Comm. DIAS no 24 (1977). · Zbl 0365.46059
[14] Feldman J..A relativistic Feynman-Kac formula. Nuclear Physics B52 (1973), 608–614.
[15] Ghirman I. I., Skorohod A. V.,The theory of stochastic processes. Vol. 2. Springer Verlag (1975).
[16] Gorini V., Kossakowski A., Sudarshan E. C. G.,Completely positive dynamicl semigroups of n-level systems. J. Mathematical Phys.17 (1976), 821.
[17] Gross L.,Logarithmic Sobolev inequalities. Amer. J. Math.97 (1976), 1061–1083. · Zbl 0318.46049
[18] Hersh R., Papanicolau G.,Non-commuting random evolutions and an opepraptoprp vpalued Feynman-Kac formula. Comm. Pure Appl. Math.25 (1972), 337–367. · Zbl 0232.60054
[19] Kac M.,On some connection between probability theory and differential and integral equations. Proc. 2nd Berkeley Symp. on Math. Stat. and Prob. (1951), 189–215.
[20] Hudson R., Ion P. D. F.,Non-commutative Feynman-Kac formulae. Proceedings of the Colloquium “Random Fields: rigorous results in statistical mechnics and quantum field theory{”. Esztergom 1979, to appear.}
[21] Kantorovich L. V., Akilov G. P.,Functional analysis (in russian). Nauka (1977). · Zbl 0127.06104
[22] Kato T.,Prturbation theory for linear opertors. Springer Verlag (1976), 2nd ed..
[23] Klein A., Landau L. J.,Singular perturbations of positivity preserving semigroups via path space tecniques. J. Functional Analysis20 (1975), 44–82. · Zbl 0335.47028
[24] Lindblad G.,On the generators of quantum dynamical semigroups. Comm. Math. Phys.48 (1976), 119–130. · Zbl 0343.47031
[25] Lindblad G.,Dissipative operators and cohomology of operator algebras. Lett. Math. Phys.1 (1976), 219–224.
[26] Malliavin P.,Formules de la moyenne, calcul de perturbations et théoremes d’annulation pour les formes harmoniques. J. Functional Analysis17 (1974), 274. · Zbl 0425.58022
[27] Nelson E.,Topics in dynamics. I: Flows. Princeton University Press (1971). · Zbl 0197.10702
[28] Osterwalder K., Schrader R.,Euclidean Fermi fields and a Feynman-Kac formula for Boson-Fermion models. Helv. Phys. Acta,46 (1973), 277–302.
[29] Pinsky M. A.,Stochastic integral representation of multiplicative operator functionals of a Wiener process. Trans. Amer. Math. Soc.167 (1972), 89–113. · Zbl 0241.60046
[30] Ray D.,On the spectra of second order differential operators. Trans. Amer. Math. Soc.77 (1954), 299–321. · Zbl 0058.32901
[31] Sakai S., C*-algebras and W*-algebras. Springer Verlag (1971).
[32] Schrader R., Uhlenbrock D. A.,Markov structures on Clifford algebras. J. Functional Analysis18 (1975), 369–413. · Zbl 0337.46062
[33] Segal I. E.,Abstract probability spaces and a theorem of Kolmogorov. Amer. J. Math.76 (1954), 721–732. · Zbl 0056.12301
[34] Simon B.,Functional integration and quantum physics. Academic Press (1979). · Zbl 0434.28013
[35] Stroock D.,On certain systems of parabolic equations. Comm. Pure Appl. Math.23 (1970), 447–457. · Zbl 0188.41103
[36] Varadhan S. R. S.,Stochastic processes. Courant Lecture Notes (1967–68).
[37] Widder D. V.,The Laplace transform. Princeton University Press (1946). · Zbl 0060.24801
[38] Wilde I. F.,The free Fermion field as a Markov field. J. Functional Analysis15 (1974), 12–21. · Zbl 0276.60095
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.