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By using F. A. Berezin’s canonical transformation method [5], we derive a nonadapted quantum stochastic differential equation (QSDE) as an equation for the strong limit of the family of unitary groups satisfying the Schrodinger equation with singularly degenerating Hamiltonians in Fock space. Stochastic differentials of QSDE generate a nonadapted associative Ito multiplication table, and the coefficients of these differentials satisfy the formal unitarity conditions of the Hudson–Parthasarathy type [10]. Introduction. The derivation of equations for quantum noise is an important problem related to applications in quantum optics, quantum information and measurement theories [1, 4, 9, 15]. The main advantage of quantum stochastic theory is an elegant implicit construction of solutions for the class of adapted QSDE describing the joint unitary evolution of a quantum system and its environment [10]. The conceptual disadvantage of this approach is a gap in understanding the unitary stochastic evolution in the spirit of the classical Stone theorem describing the infinitesimal generator of a unitary group as a self-adjoint operator. Until the recent papers [7, 8], it was not known that a unitary cocycle satisfying the QSDE can be described not by a symmetric operator but rather by a symmetrical bound1991 Mathematics Subject Classification: Primary 81S25; Secondary 47N50, 46L60. Research supported by RFBR grant N 95-01-007784 and by grant of Goskomvus of Russian Federation N 96-1.7-100 The paper is in final form and no version of it will be published elsewhere.

Quantum stochastic processes arising from the strong resolvent limits of the Schrödinger evolution in Fock space