Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Construction of quantum Dirac observables and the emergence of WKB time   We describe a method of construction of gauge-invariant operators (Dirac
observables or ``evolving constants of motion'') from the knowledge of the
eigenstates of the gauge generator in time-reparametrization invariant
mechanical systems. These invariant operators evolve unitarily with respect to
an arbitrarily chosen time variable. We emphasize that the dynamics is
relational, both in the classical and quantum theories. In this framework, we
show how the ``emergent Wentzel-Kramers-Brillouin time'' often employed in
quantum cosmology arises from a weak-coupling expansion of invariant transition
amplitudes, and we illustrate an example of singularity avoidance in a vacuum
Bianchi I (Kasner) model.

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The categories of this paper are: physics
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The categories of this paper are: econ
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The categories of this paper are: cond-mat
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The categories of this paper are: math
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The categories of this paper are: hep-lat
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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: adap-org
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The categories of this paper are: mtrl-th
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The categories of this paper are: plasm-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: chem-ph
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The categories of this paper are: q-alg
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The categories of this paper are: q-fin
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The categories of this paper are: q-bio
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The categories of this paper are: ao-sci