Path Integral Representation for Schroedinger Operators with Bernstein Functions of the Laplacian

Fumio Hiroshima, Takashi Ichinose, József Lőrinczi

Publication date: 30 May 2009

Abstract: Path integral representations for generalized Schr"odinger operators obtained under a class of Bernstein functions of the Laplacian are established. The one-to-one correspondence of Bernstein functions with L'evy subordinators is used, thereby the role of Brownian motion entering the standard Feynman-Kac formula is taken here by subordinated Brownian motion. As specific examples, fractional and relativistic Schr"odinger operators with magnetic field and spin are covered. Results on self-adjointness of these operators are obtained under conditions allowing for singular magnetic fields and singular external potentials as well as arbitrary integer and half-integer spin values. This approach also allows to propose a notion of generalized Kato class for which hypercontractivity of the associated generalized Schr"odinger semigroup is shown. As a consequence, diamagnetic and energy comparison inequalities are also derived.

This page was built for publication: Path Integral Representation for Schroedinger Operators with Bernstein Functions of the Laplacian

Report a bug (only for logged in users!)Click here to report a bug for this page (MaRDI item Q6214148)