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

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

2002-09-04

arxiv.org/abs/math-ph/0209009v2

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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