TL;DR
This paper explores the mathematical foundations of quadratic bosonic and free white noises, providing representations on interacting Fock spaces and connecting them to classical stochastic processes.
Contribution
It introduces a representation of quadratic bosonic and free white noise relations on interacting Fock spaces and links these to classical stochastic processes.
Findings
Representation of quadratic bosonic white noise on interacting Fock space
Representation of quadratic free white noise on interacting Fock space
Connection between noncommutative quadratic white noise and classical stochastic processes
Abstract
We discuss the meaning of renormalization used for deriving quadratic bosonic commutation relations introduced by Accardi and find a representation of these relations on an interacting Fock space. Also, we investigate classical stochastic processes which can be constructed from noncommutative quadratic white noise. We postulate quadratic free white noise commutation relations and find their representation on an interacting Fock space.
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