Stimulated by the quantum generalization of the canonical representation theory for Gaussian processes in \cite{AHH}, we first give the representations (not necessarily canonical) of two stationary Gaussian processes $X$ and $Y$ by means of white noises $q_t$ and $p_t$ with no assumptions on their commutator. We then assume that $q_t+ip_t$ annihilates the vacuum state and prove that the representations are the joint Boson Fock ones if and only if $X$ and $Y$ have a scalar commutator.
Accardi, L., Hibino, Y. (2002). Canonical representation of stationary quantum Gaussian processes. INFINITE DIMENSIONAL ANALYSIS QUANTUM PROBABILITY AND RELATED TOPICS, 5(3), 1-8 [10.1142/S0219025702000869].
Canonical representation of stationary quantum Gaussian processes
ACCARDI, LUIGI;
2002-01-01
Abstract
Stimulated by the quantum generalization of the canonical representation theory for Gaussian processes in \cite{AHH}, we first give the representations (not necessarily canonical) of two stationary Gaussian processes $X$ and $Y$ by means of white noises $q_t$ and $p_t$ with no assumptions on their commutator. We then assume that $q_t+ip_t$ annihilates the vacuum state and prove that the representations are the joint Boson Fock ones if and only if $X$ and $Y$ have a scalar commutator.| File | Dimensione | Formato | |
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