Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Spacetime Quantum Mechanics and the Quantum Mechanics of Spacetime   These are the author's lectures at the 1992 Les Houches Summer School,
"Gravitation and Quantizations". They develop a generalized sum-over-histories
quantum mechanics for quantum cosmology that does not require either a
preferred notion of time or a definition of measurement. The "post-Everett"
quantum mechanics of closed systems is reviewed. Generalized quantum theories
are defined by three elements (1) the set of fine-grained histories of the
closed system which are its most refined possible description, (2) the allowed
coarse grainings which are partitions of the fine-grained histories into
classes, and (3) a decoherence functional which measures interference between
coarse grained histories. Probabilities are assigned to sets of alternative
coarse-grained histories that decohere as a consequence of the closed system's
dynamics and initial condition. Generalized sum-over histories quantum theories
are constructed for non-relativistic quantum mechanics, abelian gauge theories,
a single relativistic world line, and for general relativity. For relativity
the fine-grained histories are four-metrics and matter fields. Coarse grainings
are four-dimensional diffeomorphism invariant partitions of these. The
decoherence function is expressed in sum-over-histories form. The quantum
mechanics of spacetime is thus expressed in fully spacetime form. The
coarse-grainings are most general notion of alternative for quantum theory
expressible in spacetime terms. Hamiltonian quantum mechanics of matter fields
with its notion of unitarily evolving state on a spacelike surface is recovered
as an approximation to this generalized quantum mechanics appropriate for those
initial conditions and coarse-grainings such that spacetime geometry

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The categories of this paper are: chem-ph
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The categories of this paper are: q-bio
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The categories of this paper are: math-ph
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The categories of this paper are: stat
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The categories of this paper are: hep-ph
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The categories of this paper are: physics
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The categories of this paper are: cond-mat
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The categories of this paper are: nlin
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The categories of this paper are: q-alg
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The categories of this paper are: comp-gas
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The categories of this paper are: hep-lat
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The categories of this paper are: solv-int
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The categories of this paper are: patt-sol
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The categories of this paper are: econ
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The categories of this paper are: q-fin
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The categories of this paper are: dg-ga