Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Quantum Propagator for a Nonrelativistic Particle in the Vicinity of
  a Time Machine   We study the propagator of a non-relativistic, non-interacting particle in
any non-relativistic ``time-machine'' spacetime of the type shown in Fig.~1: an
external, flat spacetime in which two spatial regions, $V_-$ at time $t_-$ and
$V_+$ at time $t_+$, are connected by two temporal wormholes, one leading from
the past side of $V_-$ to t the future side of $V_+$ and the other from the
past side of $V_+$ to the future side of $V_-$. We express the propagator
explicitly in terms of those for ordinary, flat spacetime and for the two
wormholes; and from that expression we show that the propagator satisfies
completeness and unitarity in the initial and final ``chronal regions''
(regions without closed timelike curves) and its propagation from the initial
region to the final region is unitary. However, within the time machine it
satisfies neither completeness nor unitarity. We also give an alternative proof
of initial-region-to-final-region unitarity based on a conserved current and
Gauss's theorem. This proof can be carried over without change to most any
non-relativistic time-machine spacetime; it is the non-relativistic version of
a theorem by Friedman, Papastamatiou and Simon, which says that for a free
scalar field, quantum mechanical unitarity follows from the fact that the
classical evolution preserves the Klein-Gordon inner product.

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The categories of this paper are: mtrl-th
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The categories of this paper are: atom-ph
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The categories of this paper are: econ
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The categories of this paper are: cs
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The categories of this paper are: chem-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: cond-mat
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The categories of this paper are: cmp-lg
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The categories of this paper are: hep-lat
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The categories of this paper are: q-fin
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The categories of this paper are: nlin
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The categories of this paper are: adap-org
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The categories of this paper are: solv-int
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The categories of this paper are: physics
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The categories of this paper are: dg-ga
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The categories of this paper are: q-alg