The notion of mutual quadratic variation (square bracket) is extended to a quantum probabilistic framework. The mutual quadratic variations of the annihilation, creation, and number fields in a Gaussian representation are calculated, in both the Boson and the Fermion case, in the strong apology on a common invariant domain. It is proved that the corresponding Ito table closes at the second order. The Fock representation is characterized, among the Gaussian ones, by the property that its Ito table closes at the first order.
Accardi, L., Quaegebeur, J. (1989). The Ito algebra of quantum Gaussian fields. JOURNAL OF FUNCTIONAL ANALYSIS, 85(2), 213-263.
The Ito algebra of quantum Gaussian fields
ACCARDI, LUIGI;
1989-01-01
Abstract
The notion of mutual quadratic variation (square bracket) is extended to a quantum probabilistic framework. The mutual quadratic variations of the annihilation, creation, and number fields in a Gaussian representation are calculated, in both the Boson and the Fermion case, in the strong apology on a common invariant domain. It is proved that the corresponding Ito table closes at the second order. The Fock representation is characterized, among the Gaussian ones, by the property that its Ito table closes at the first order.| File | Dimensione | Formato | |
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AcQu88_Ito algebra of QGF.pdf
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