Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Quantum Field Theory on Curved Backgrounds, I. The Euclidean Functional
  Integral   We give a mathematical construction of Euclidean quantum field theory on
certain curved backgrounds. We focus on generalizing Osterwalder-Schrader
quantization, as these methods have proved useful to establish estimates for
interacting fields on flat space-times. In this picture, a static Killing
vector generates translations in Euclidean time, and physical positivity is
played by positivity under reflection of Euclidean time. We discuss the
quantization of flows which correspond to classical space-time symmetries, and
give a general set of conditions which imply that broad classes of operators in
the classical picture give rise to well-defined operators on the quantum-field
Hilbert space. In particular, Killing fields on spatial sections give rise to
unitary groups on the quantum-field Hilbert space, and corresponding
densely-defined self-adjoint generators. We construct the Schr\"odinger
representation using a method which involves localizing certain integrals over
the full manifold to integrals over a codimension-one submanifold. This method
is called sharp-time localization, and implies reflection positivity.

36
The categories of this paper are: cmp-lg
32
The categories of this paper are: atom-ph
4
The categories of this paper are: cond-mat
19
The categories of this paper are: eess
26
The categories of this paper are: bayes-an
9
The categories of this paper are: nlin
30
The categories of this paper are: q-alg
37
The categories of this paper are: supr-con
3
The categories of this paper are: physics
35
The categories of this paper are: mtrl-th
29
The categories of this paper are: funct-an
27
The categories of this paper are: comp-gas
22
The categories of this paper are: chao-dyn
11
The categories of this paper are: hep-lat
13
The categories of this paper are: quant-ph
1
The categories of this paper are: cs