Spacetime coarse grainings in nonrelativistic quantum mechanics

Journal Article · Fri Nov 15 04:00:00 EST 1991 · Physical Review, D (Particles Fields); (United States)

DOI:https://doi.org/10.1103/PhysRevD.44.3173· OSTI ID:6261243

Hartle, J B ^[1]

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1. Department of Physics, University of California, Santa Barbara, California (USA)

Sum-over-histories generalizations of nonrelativistic quantum mechanics are explored in which probabilities are predicted, not just for alternatives defined on spacelike surfaces, but for alternatives defined by the behavior of spacetime histories with respect to spacetime regions. Closed, nonrelativistic systems are discussed whose histories are paths in a given configuration space. The action and the initial quantum state are assumed fixed and given. A formulation of quantum mechanics is used which assigns probabilities to members of sets of alternative coarse-grained histories of the system, that is, to the individual classes of a partition of its paths into exhaustive and exclusive classes. Probabilities are assigned to those sets which decohere, that is, whose probabilities are consistent with the sum rules of probability theory. Coarse graining by the behavior of paths with respect to regions of spacetime is described. For example, given a single region, the set of all paths may be partitioned into those which never pass through the region and those which pass through the region at least once. A sum-over-histories decoherence functional is defined for sets of alternative histories coarse-grained by spacetime regions. Techniques for the definition and effective computation of the relevant sums over histories by operator-product formulas are described and illustrated by examples. Methods based on Euclidean stochastic processes are also discussed and illustrated. Models of decoherence and measurement for spacetime coarse grainings are described. Issues of causality are investigated. Such spacetime generalizations of nonrelativistic quantum mechanics may be useful models for a generalized quantum mechanics of spacetime geometry.

• OSTI ID: 6261243
• Journal Information: Physical Review, D (Particles Fields); (United States), Journal Name: Physical Review, D (Particles Fields); (United States) Vol. 44:10; ISSN PRVDA; ISSN 0556-2821
• Country of Publication: United States
• Language: English

Related Subjects

661100* -- Classical & Quantum Mechanics-- (1992-)
661300 -- Other Aspects of Physical Science-- (1992-)
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
CAUSALITY
COSMOLOGY
EQUATIONS
EUCLIDEAN SPACE
FEYNMAN PATH INTEGRAL
HAMILTONIANS
INTEGRALS
MATHEMATICAL OPERATORS
MATHEMATICAL SPACE
MECHANICS
PROBABILITY
QUANTUM MECHANICS
QUANTUM OPERATORS
RIEMANN SPACE
SPACE
SPACE-TIME
STOCHASTIC PROCESSES
SUM RULES
UNIVERSE