Construction of self-adjoint Berezin-Toeplitz operators on Kähler manifolds and a probabilistic representation of the associated semigroups (Q1400159)

This paper is devoted to the study of Berezin-Toeplitz operators defined on the Hilbert space. The author develops self-adjointness criteria for Berezin-Toeplitz operators defined via quadratic forms, obtains regularity conditions for possibly unbounded classical Hamiltonians ensuring that their quantum analogs are self-adjoint operators, generalizes an approach to path integral quantization, and discusses the case of unbounded Berezin-Toeplitz operators and non-compact manifolds. Moreover, a relationship between Berezin-Toeplitz and Schrödinger operators is established and the probabilistic repersentation of the semigroup generated by selfadjoint, semibounded Berezin-Toeplitz operators is considered.