Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Probabilistic Representation and Fall-Off of Bound States of
  Relativistic Schr\"odinger Operators with Spin 1/2   A Feynman-Kac type formula of relativistic Schr\"odinger operators with
unbounded vector potential and spin 1/2 is given in terms of a three-component
process consisting of Brownian motion, a Poisson process and a subordinator.
This formula is obtained for unbounded magnetic fields and magnetic field with
zeros. From this formula an energy comparison inequality is derived. Spatial
decay of bound states is established separately for growing and decaying
potentials by using martingale methods.

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The categories of this paper are: ao-sci
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The categories of this paper are: acc-phys
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The categories of this paper are: adap-org
18
The categories of this paper are: econ
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The categories of this paper are: dg-ga
15
The categories of this paper are: nucl-ex
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The categories of this paper are: chem-ph
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The categories of this paper are: comp-gas
8
The categories of this paper are: hep-ex
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The categories of this paper are: nlin
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The categories of this paper are: bayes-an
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The categories of this paper are: eess
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The categories of this paper are: supr-con
0
The categories of this paper are: hep-ph
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The categories of this paper are: hep-th
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The categories of this paper are: mtrl-th