  Following Dirac, the rules of canonical quantization include classical and
quantum contact transformations of classical and quantum phase space variables.
While arbitrary classical canonical coordinate transformations exist that is
not the case for some analogous quantum canonical coordinate transformations.
This failure is due to the rigid connection of quantum variables arising by
promoting the corresponding classical variable from a $c$-number to a
$q$-number. A different relationship of $c$-numbers and $q$-numbers in the
procedures of Enhanced Quantization shows the compatibility of all quantum
operators with all classical canonical coordinate transformations.
