On Quantum Ito Algebras and their decompositions

Simple item page
dc.creatorBelavkin, V. P.
dc.date2005-12-21
dc.date.accessioned2026-07-07T06:54:40Z
dc.date.available2026-07-07T06:54:40Z
dc.descriptionA simple axiomatic characterization of the noncommutative Ito algebra is given and a pseudo-Euclidean fundamental representation for such algebra is described. It is proved that every quotient Ito algebra has a faithful representation in a Minkowski space and is canonically decomposed into the orthogonal sum of quantum Brownian (Wiener) algebra and quantum Levy (Poisson) algebra. In particular, every quantum thermal noise of a finite number of degrees of freedom is the orthogonal sum of a quantum Wiener noise and a quantum Poisson noise as it is stated by the Levy-Khinchin theorem in the classical case. Two basic examples of non-commutative Ito finite group algebras are considered.
dc.description13 pages. See related papers at http://www.maths.nott.ac.uk/personal/vpb/research/cha_noi.html http://www.maths.nott.ac.uk/personal/vpb/research/ana_cal.html
dc.identifierhttps://arxiv.org/abs/math-ph/0512071
dc.identifierhttp://arxiv.org/abs/math-ph/0512071
dc.identifierLetters in Mathematical Physics 45 (1998) 131--145
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/106021
dc.subjectMathematical Physics
dc.titleOn Quantum Ito Algebras and their decompositions
dc.typetext

Files

Collections

arXiv