On Quantum Ito Algebras and their decompositions
Belavkin, V. P.
arXiv, 0512071 / Harvested from arXiv
Text on arXiv
A 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.
Publié le : 2005-12-21
Classification:  Mathematical Physics 
@article{0512071,
     author = {Belavkin, V. P.},
     title = {On Quantum Ito Algebras and their decompositions},
     journal = {arXiv},
     volume = {2005},
     number = {0},
     year = {2005},
     language = {en},
     url = {http://dml.mathdoc.fr/item/0512071}
}

Belavkin, V. P. On Quantum Ito Algebras and their decompositions. arXiv, Tome 2005 (2005) no. 0, . http://gdmltest.u-ga.fr/item/0512071/