Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Unified Scheme for Generalized Sectors based on Selection Criteria
  --Order parameters of symmetries and of thermality and physical meanings of
  adjunctions--   A unified scheme for treating generalized superselection sectors is proposed
on the basis of the notion of selection criteria to characterize states of
relevance to each specific domain in quantum physics, ranging from the
relativistic quantum fields in the vacuum situations with unbroken and
spontaneously broken internal symmetries, through equilibrium and
non-equilibrium states to some basic aspects in measurement processes. This is
achieved by the help of c-q and q-c channels: the former determines the states
to be selected and to be parametrized by the order parameters, and the latter
provides the physical interpretations of selected states in terms of order
parameters. This formulation extends the traditional range of applicability of
the Doplicher-Roberts construction method for recovering the field algebra and
the gauge group (of the first kind) from the data of group invariant
observables to the situations with spontaneous symmetry breakdown: in use of
the machinery proposed, the physical and mathematical meaning of basic
structural ingredients associated with the spontaneously broken symmetry are
re-examined, such as the degenerate vacua parametrized by the variable
belonging to the relevant homogeneous space, the Goldstone modes and
condensates, etc. The geometrical meaning of the space of order parameters is
naturally understood in relation with the adjunction as the classifying space
of a sector structure. As further examples of applications, some basic notions
arising in the mathematical framework of quantum theory are reformulated and
examined in connection with control theory.

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The categories of this paper are: cs
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The categories of this paper are: plasm-ph
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The categories of this paper are: astro-ph
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The categories of this paper are: stat
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The categories of this paper are: solv-int
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The categories of this paper are: hep-lat
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The categories of this paper are: nlin
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The categories of this paper are: adap-org
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The categories of this paper are: q-alg
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The categories of this paper are: bayes-an
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The categories of this paper are: hep-ex
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The categories of this paper are: econ
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The categories of this paper are: comp-gas
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The categories of this paper are: nucl-th
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The categories of this paper are: quant-ph
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The categories of this paper are: gr-qc