Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Ground state and functional integral representations of the CCR algebra
  with free evolution   The problem of existence of ground state representations on the CCR algebra
with free evolution are discussed and all the solutions are classified in terms
of non regular or indefinite invariant functionals. In both cases one meets
unusual mathematical structures which appear as prototypes of phenomena typical
of gauge quantum field theory, in particular of the temporal gauge. The
functional integral representation in the positive non regular case is
discussed in terms of a generalized stochastic process satisfying the Markov
property. In the indefinite case the unique time translation and scale
invariant Gaussian state is surprisingly faithful and its GNS representation is
characterized in terms of a KMS operator. In the corresponding Euclidean
formulation, one has a generalization of the Osterwalder-Schrader
reconstruction and the indefinite Nelson space, defined by the Schwinger
functions, has a unique Krein structure, allowing for the construction of
Nelson projections, which satisfy the Markov property. Even if Nelson
positivity is lost, a functional integral representation of the Schwinger
functions exists in terms of a Wiener random variable and a Gaussian complex
variable.

19
The categories of this paper are: eess
35
The categories of this paper are: mtrl-th
24
The categories of this paper are: dg-ga
33
The categories of this paper are: plasm-ph
11
The categories of this paper are: hep-lat
4
The categories of this paper are: cond-mat
36
The categories of this paper are: cmp-lg
10
The categories of this paper are: q-bio
31
The categories of this paper are: ao-sci
29
The categories of this paper are: funct-an
8
The categories of this paper are: hep-ex
12
The categories of this paper are: nucl-th
13
The categories of this paper are: quant-ph
23
The categories of this paper are: solv-int
7
The categories of this paper are: hep-th
27
The categories of this paper are: comp-gas