  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).
