Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Models of free quantum field theories on curved backgrounds   Free quantum field theories on curved backgrounds are discussed via three
explicit examples: the real scalar field, the Dirac field and the Proca field.
The first step consists of outlining the main properties of globally hyperbolic
spacetimes, that is the class of manifolds on which the classical dynamics of
all physically relevant free fields can be written in terms of a Cauchy
problem. The set of all smooth solutions of the latter encompasses the
dynamically allowed configurations which are used to identify via a suitable
pairing a collection of classical observables. As a last step we use such
collection to construct a $*$-algebra which encodes the information on the
dynamics and on the canonical commutation or anti-commutation relations
depending whether the underlying field is a Fermion or a Boson.

6
The categories of this paper are: astro-ph
27
The categories of this paper are: comp-gas
9
The categories of this paper are: nlin
34
The categories of this paper are: chem-ph
8
The categories of this paper are: hep-ex
16
The categories of this paper are: stat
21
The categories of this paper are: adap-org
19
The categories of this paper are: eess
32
The categories of this paper are: atom-ph
25
The categories of this paper are: patt-sol
17
The categories of this paper are: q-fin
13
The categories of this paper are: quant-ph
28
The categories of this paper are: alg-geom
22
The categories of this paper are: chao-dyn
11
The categories of this paper are: hep-lat
35
The categories of this paper are: mtrl-th