Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: An index theorem on asymptotically static spacetimes with compact Cauchy
  surface   We consider the Dirac operator on asymptotically static Lorentzian manifolds
with an odd-dimensional compact Cauchy surface. We prove that if
Atiyah-Patodi-Singer boundary conditions are imposed at infinite times then the
Dirac operator is Fredholm. This generalizes a theorem due to B\"ar-Strohmaier
in the case of finite times, and we also show that the corresponding index
formula extends to the infinite setting. Furthermore, we demonstrate the
existence of a Fredholm inverse which is at the same time a Feynman parametrix
in the sense of Duistermaat-H\"ormander. The proof combines methods from
time-dependent scattering theory with a variant of Egorov's theorem for
pseudo-differential hyperbolic systems.

28
The categories of this paper are: alg-geom
33
The categories of this paper are: plasm-ph
21
The categories of this paper are: adap-org
37
The categories of this paper are: supr-con
0
The categories of this paper are: hep-ph
16
The categories of this paper are: stat
29
The categories of this paper are: funct-an
3
The categories of this paper are: physics
22
The categories of this paper are: chao-dyn
5
The categories of this paper are: gr-qc
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The categories of this paper are: ao-sci
14
The categories of this paper are: math-ph
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The categories of this paper are: eess
18
The categories of this paper are: econ
30
The categories of this paper are: q-alg
34
The categories of this paper are: chem-ph