Emergent Classicality via Commuting Position and Momentum Operators

Details Emergent Classicality via Commuting Position and Momentum Operators Emergent Classicality via Commuting Position and Momentum Operators

2009-03-10

arxiv.org/abs/0903.1799v1

J.Phys. Conf.Ser 174, 012005 (2009)

Physics

Quantum Physics

To appear in Proceedings of the 2008 DICE Conference

Scientific paper

Any account of the emergence of classicality from quantum theory must address the fact that the quantum operators representing positions and momenta do not commute, whereas their classical counterparts suffer no such restrictions. To address this, we revive an old idea of von Neumann, and seek a pair of commuting operators $X,P$ which are, in a specific sense, "close" to the canonical non-commuting 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 limited by the Balian-Low theorem. Here these limitations are avoided by restricting attention to situations in which the density matrix is reasonably decohered (i.e., spread out in phase space).

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