Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Metaplectic sheets and caustic traversals in the Weyl representation   The quantum Hamiltonian generates in time a family of evolution operators.
Continuity of this family holds within any choice of representation and, in
particular, for the Weyl propagator, even though its simplest semiclassical
approximation may develop caustic singularities. The phase jumps of the Weyl
propagator across caustics have not been previously determined.
  The semiclassical appproximation relies on individual classical trajectories
together with their neighbouring tangent map. Based on the latter, one defines
a continuous family of unitary tangent propagators, with an exact Weyl
representation that is close to the full semiclassical approximation in an
appropriate neighbourhood. The phase increment of the semiclassical Weyl
propagator, as a caustic is crossed, is derived from the facts that the
corresponding family of tangent operators belong to the metaplectic group and
that the products of the tangent propagators are obtained from Gaussian
integrals. The Weyl representation of the metaplectic group is here presented,
with the correct phases determined within an intrinsic ambiguity for the
overall sign. The elements that fully determine the phase increment across a
particular caustic are then analysed.

8
The categories of this paper are: hep-ex
28
The categories of this paper are: alg-geom
23
The categories of this paper are: solv-int
22
The categories of this paper are: chao-dyn
25
The categories of this paper are: patt-sol
1
The categories of this paper are: cs
30
The categories of this paper are: q-alg
37
The categories of this paper are: supr-con
35
The categories of this paper are: mtrl-th
18
The categories of this paper are: econ
9
The categories of this paper are: nlin
0
The categories of this paper are: hep-ph
5
The categories of this paper are: gr-qc
12
The categories of this paper are: nucl-th
6
The categories of this paper are: astro-ph
34
The categories of this paper are: chem-ph