Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Gutzwiller Trace Formula for Quantum Systems with Spin   The Gutzwiller trace formula provides a semiclassical approximation for the
density of states of a quantum system in terms of classical periodic orbits. In
its original form Gutzwiller derived the trace formula for quantum systems
without spin. We will discuss the modifications that arise for quantum systems
with both translational and spin degrees of freedom and which are either
described by Pauli- or Dirac-Hamiltonians. In addition, spectral densities
weighted by expectation values of observables will be considered. It turns out
that in all cases the semiclassical approximation yields sums over periodic
orbits of the translational motion. Spin contributes via weight factors that
take a spin precession along the translational orbits into account.

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The categories of this paper are: funct-an
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The categories of this paper are: cond-mat
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The categories of this paper are: acc-phys
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The categories of this paper are: econ
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The categories of this paper are: mtrl-th
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The categories of this paper are: ao-sci
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The categories of this paper are: physics
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The categories of this paper are: q-alg
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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: eess
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The categories of this paper are: hep-th
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The categories of this paper are: chem-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: nucl-ex
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The categories of this paper are: adap-org