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Chaotic decompositions in \(\mathbb{Z}_2\)-graded quantum stochastic calculus. (English) Zbl 0926.46051

Alicki, Robert (ed.) et al., Quantum probability. Workshop, Gdańsk, Poland, July 1–6, 1997. Warsaw: Polish Academy of Sciences, Institute of Mathematics, Banach Cent. Publ. 43, 167-174 (1998).
Summary: A brief introduction to \(\mathbb{Z}_2\)-graded quantum stochastic calculus is given. By inducing a superalgebraic structure on the space of iterated integrals and using the heuristic classical relation \(df(\Lambda)= f(\Lambda+ d\Lambda)- f(\Lambda)\) we provide an explicit formula for chaotic expansions of polynomials of the integrator processes of \(\mathbb{Z}_2\)-graded quantum stochastic calculus.
For the entire collection see [Zbl 0903.00097].

MSC:

46L60 Applications of selfadjoint operator algebras to physics
81S25 Quantum stochastic calculus
46L53 Noncommutative probability and statistics
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