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The Ito algebra of quantum Gaussian fields. (English) Zbl 0669.60099

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 topology 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.

MSC:

60K35 Interacting random processes; statistical mechanics type models; percolation theory
81P20 Stochastic mechanics (including stochastic electrodynamics)
46L51 Noncommutative measure and integration
46L53 Noncommutative probability and statistics
46L54 Free probability and free operator algebras
60H99 Stochastic analysis
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References:

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