Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Path Integral Representation for Schroedinger Operators with Bernstein
  Functions of the Laplacian   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.

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The categories of this paper are: cond-mat
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The categories of this paper are: ao-sci
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The categories of this paper are: hep-th
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The categories of this paper are: nucl-ex
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The categories of this paper are: gr-qc
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The categories of this paper are: nlin
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The categories of this paper are: hep-ex
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The categories of this paper are: mtrl-th
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The categories of this paper are: physics
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The categories of this paper are: chao-dyn
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The categories of this paper are: hep-lat
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The categories of this paper are: eess
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The categories of this paper are: econ
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The categories of this paper are: acc-phys
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The categories of this paper are: comp-gas
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The categories of this paper are: q-alg