Time-orthogonal unitary dilations and noncommutative Feynman-Kac formulae
dc.contributor.author | Hudson, R. L. | en_US |
dc.contributor.author | Parthasarathy, K. R. | en_US |
dc.contributor.author | Ion, P. D. F. | en_US |
dc.date.accessioned | 2006-09-11T17:53:19Z | |
dc.date.available | 2006-09-11T17:53:19Z | |
dc.date.issued | 1982-02 | en_US |
dc.identifier.citation | Hudson, R. L.; Ion, P. D. F.; Parthasarathy, K. R.; (1982). "Time-orthogonal unitary dilations and noncommutative Feynman-Kac formulae." Communications in Mathematical Physics 83(2): 261-280. <http://hdl.handle.net/2027.42/46525> | en_US |
dc.identifier.issn | 1432-0916 | en_US |
dc.identifier.issn | 0010-3616 | en_US |
dc.identifier.uri | https://hdl.handle.net/2027.42/46525 | |
dc.description.abstract | An analysis of Feynman-Kac formulae reveals that, typically, the unperturbed semigroup is expressed as the expectation of a random unitary evolution and the perturbed semigroup is the expectation of a perturbation of this evolution in which the latter perturbation is effected by a cocycle with certain covariance properties with respect to the group of translations and reflections of the line. We consider generalisations of the classical commutative formalism in which the probabilistic properties are described in terms of non-commutative probability theory based on von Neumann algebras. Examples of this type are generated, by means of second quantisation, from a unitary dilation of a given self-adjoint contraction semigroup, called the time orthogonal unitary dilation, whose key feature is that the dilation operators corresponding to disjoint time intervals act nontrivially only in mutually orthogonal supplementary Hilbert spaces. | en_US |
dc.format.extent | 1014787 bytes | |
dc.format.extent | 3115 bytes | |
dc.format.mimetype | application/pdf | |
dc.format.mimetype | text/plain | |
dc.language.iso | en_US | |
dc.publisher | Springer-Verlag | en_US |
dc.subject.other | Statistical Physics | en_US |
dc.subject.other | Quantum Physics | en_US |
dc.subject.other | Physics | en_US |
dc.subject.other | Mathematical and Computational Physics | en_US |
dc.subject.other | Quantum Computing, Information and Physics | en_US |
dc.subject.other | Nonlinear Dynamics, Complex Systems, Chaos, Neural Networks | en_US |
dc.subject.other | Relativity and Cosmology | en_US |
dc.title | Time-orthogonal unitary dilations and noncommutative Feynman-Kac formulae | en_US |
dc.type | Article | en_US |
dc.subject.hlbsecondlevel | Physics | en_US |
dc.subject.hlbsecondlevel | Mathematics | en_US |
dc.subject.hlbtoplevel | Science | en_US |
dc.description.peerreviewed | Peer Reviewed | en_US |
dc.contributor.affiliationum | Mathematical Reviews, University of Michigan, 611 Church Street, 48109, Ann Arbor, MI, USA | en_US |
dc.contributor.affiliationother | Mathematics Department, University of Nottingham, NG7 2RD, University Park, Nottingham, England | en_US |
dc.contributor.affiliationother | Indian Statistical Institute, 7, S.J.S. Sansanwal Marg, 110016, New Dehli, India | en_US |
dc.contributor.affiliationumcampus | Ann Arbor | en_US |
dc.description.bitstreamurl | http://deepblue.lib.umich.edu/bitstream/2027.42/46525/1/220_2005_Article_BF01976044.pdf | en_US |
dc.identifier.doi | http://dx.doi.org/10.1007/BF01976044 | en_US |
dc.identifier.source | Communications in Mathematical Physics | en_US |
dc.owningcollname | Interdisciplinary and Peer-Reviewed |
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