zbMATH — the first resource for mathematics

Time-orthogonal unitary dilations and noncommutative Feynman-Kac formulae. (English) Zbl 0485.46038

46L60 Applications of selfadjoint operator algebras to physics
81P20 Stochastic mechanics (including stochastic electrodynamics)
47D03 Groups and semigroups of linear operators
Full Text: DOI
[1] Accardi, L.: On the quantum Feynman-Kac formula (preprint) · Zbl 0437.60030
[2] Accardi, L., Frigerio, A., Lewis, J.T.: Quantum stochastic processes (preprint) · Zbl 0498.60099
[3] Cockroft, A.M., Hudson, R.L.: Quantum mechanical Wiener processes. J. Multivar. Anal.7, 107–124 (1978) · Zbl 0401.60086
[4] Davies, E.B.: Some contraction semigroups in quantum probability. Z. Wahrsch. Verw. Geb.23, 261–273 (1972) · Zbl 0231.20023
[5] Evans, D.E., Lewis, J.T.: Dilations of irreversible evolutions in algebraic quantum theory. Commun. Dublin Inst. for Adv. Studies, Series A24 (1974) · Zbl 0365.46059
[6] Guichardet, A.: Symmetric Hilbert spaces and related topics. In: Lecture Notes in Mathematics, Vol. 261. Berlin, Heidelberg, New York: Springer 1972 · Zbl 0265.43008
[7] Hudson, R.L., Ion, P.D.F.: The Feynman-Kac formula for a canonical quantum mechanical Wiener process, to appear in Proceedings of the Esztergom (1979) Colloquium ”Random fields: rigorous results in statistical mechanics and quantum field theory”
[8] Hudson, R.L., Ion, P.D.F., Parthasarathy, K.R.: The Feynman-Kac formula for Boson Wiener processes. In: Quantum mechanics in mathematics, physics, and chemistry. Gustafson, K., et al. (ed.). New York: Plenum Press 1981
[9] Hunt, G.A.: Semigroups of measures on Lie groups. Trans. Am. Math. Soc.81, 264–293 (1956) · Zbl 0073.12402
[10] Lax, P., Phillips, R.S.: Scattering theory. New York: Academic Press 1964 · Zbl 0117.09104
[11] Parthasarathy, K.R.: Probability measures on metric spaces. New York: Academic Press 1967 · Zbl 0153.19101
[12] Phillips, R.S.: Perturbation theory of semigroups of linear operators. Trans. Am. Math. Soc.74, 199–220 (1953)
[13] Simon, B.: Functional integration and quantum physics. New York: Academic Press 1979 · Zbl 0434.28013
[14] Sz-Nagy, B., Foias, C.: Harmonic analysis of operators on Hilbert space. Amsterdam: North-Holland 1970 · Zbl 0201.45003
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.