On q-deformed quantum stochastic calculus
Sniady, Piotr
arXiv, 0007035 / Harvested from arXiv
Text on arXiv
In this paper we investigate a quantum stochastic calculus build of creation, annihilation and number of particles operators which fulfill some deformed commutation relations. Namely, we introduce a deformation of a number of particles operator which has simple commutation relations with well known q-deformed creation and annihilation operators. Since all operators considered in this theory are bounded we do not deal with some difficulties of a non deformed theory of Hudson and Parthasarathy. We define stochastic integrals and estimate them in the operator norm. We prove Ito's formula as well.
Publié le : 2000-07-26
Classification:  Mathematical Physics,  Mathematics - Probability,  Mathematics - Quantum Algebra,  81S25,  05A30 
@article{0007035,
     author = {Sniady, Piotr},
     title = {On q-deformed quantum stochastic calculus},
     journal = {arXiv},
     volume = {2000},
     number = {0},
     year = {2000},
     language = {en},
     url = {http://dml.mathdoc.fr/item/0007035}
}

Sniady, Piotr. On q-deformed quantum stochastic calculus. arXiv, Tome 2000 (2000) no. 0, . http://gdmltest.u-ga.fr/item/0007035/