Physics – Mathematical Physics
Scientific paper
2002-09-04
Physics
Mathematical Physics
AMS-LaTeX, 14 pages, no figures, v.2: added reference in introduction, added remark in Examples 3.6.2
Scientific paper
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 Schr\"odinger operators that was recently generalized to Riemannian manifolds [Wittich, J. Math. Phys. {\bf 41} (2000), 244].
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