Commuting position and momentum operators, exact decoherence, and emergent classicality

Journal Article · Sat Oct 15 04:00:00 EDT 2005 · Physical Review. A

DOI:https://doi.org/10.1103/PhysRevA.72.042109· OSTI ID:20718689

Halliwell, J J ^[1]

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1. Blackett Laboratory, Imperial College, London SW7 2BZ (United Kingdom)

Inspired by an old idea of von Neumann, we seek a pair of commuting operators X, P which are, in a specific sense, 'close' to the canonical noncommuting position and momentum operators x, p. The construction of such operators is related to the problem of finding complete sets of orthonormal phase-space-localized states, a problem severely constrained by the Balian-Low theorem. Here these constraints are avoided by restricting attention to situations in which the density matrix is reasonably decohered (i.e., spread out in phase space). Commuting position and momentum operators are argued to be of use in discussions of emergent classicality from quantum mechanics. In particular, they may be used to give a discussion of the relationship between exact and approximate decoherence in the decoherent-histories approach to quantum theory.

• OSTI ID: 20718689
• Journal Information: Physical Review. A, Journal Name: Physical Review. A Journal Issue: 4 Vol. 72; ISSN 1050-2947; ISSN PLRAAN
• Country of Publication: United States
• Language: English

Related Subjects

74 ATOMIC AND MOLECULAR PHYSICS
COMMUTATION RELATIONS
DENSITY MATRIX
PHASE SPACE
QUANTUM DECOHERENCE
QUANTUM MECHANICS
QUANTUM OPERATORS