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A transformation formula relating resolvents of Berezin-Toeplitz operators by an invariance property of Brownian motion

Bernhard G. Bodmann

math-pharXiv:math-ph/0209009

Abstract

Using a stochastic representation provided by Wiener-regularized path integrals for the semigroups generated by certain Berezin-Toeplitz operators, a transformation formula for their resolvents is derived. The key property used in the transformation of the stochastic representation is that, up to a time change, Brownian motion is invariant under harmonic morphisms. This result for Berezin-Toeplitz operators is obtained in analogy with a well-known technique generating relations among Schrödinger operators that was recently generalized to Riemannian manifolds [Wittich, J. Math. Phys. 41 (2000), 244].

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