Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Inequivalent representations of commutator or anticommutator rings of
  field operators and their applications   Hamiltonian of a system in quantum field theory can give rise to infinitely
many partition functions which correspond to infinitely many inequivalent
representations of the canonical commutator or anticommutator rings of field
operators. This implies that the system can theoretically exist in infinitely
many Gibbs states. The system resides in the Gibbs state which corresponds to
its minimal Helmholtz free energy at a given range of the thermodynamic
variables. Individual inequivalent representations are associated with
different thermodynamic phases of the system. The BCS Hamiltonian of
superconductivity is chosen to be an explicit example for the demonstration of
the important role of inequivalent representations in practical applications.
Its analysis from the inequivalent representations' point of view has led to a
recognition of a novel type of the superconducting phase transition.

32
The categories of this paper are: atom-ph
26
The categories of this paper are: bayes-an
36
The categories of this paper are: cmp-lg
3
The categories of this paper are: physics
10
The categories of this paper are: q-bio
28
The categories of this paper are: alg-geom
31
The categories of this paper are: ao-sci
15
The categories of this paper are: nucl-ex
12
The categories of this paper are: nucl-th
14
The categories of this paper are: math-ph
2
The categories of this paper are: math
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
8
The categories of this paper are: hep-ex
18
The categories of this paper are: econ