  The generalization of the Nelson-Halperin-Young theory of 2D melting to the
dynamical 2+1D quantum case is presented. The bosonic quantum crystal dualizes
in superfluids or superconductors exhibiting nematic liquid crystalline orders,
corresponding with bose condensates of dislocations exhibiting a dual shear
Meissner-Higgs mechanism. The topologically ordered nematic phase suggested by
Lammert, Toner and Rokshar finds a simple interpretation in this framework. The
ordered nematic is a true quantum phase: the dynamical glide principle
interferes with the effect that the phonon spectrum of the crystal re-emerges
in the direction orthogonal to the director. Novel insights follow from the
duality on the fundamental nature of superfluidity and superconductivity. The
superfluid can be viewed as an elastic medium having lost its rigidity against
shear stresses. Upon dualizing the electrically charged crystal the
electromagnetic Meissner phase is recovered, showing peculiar screening current
oscillations when the shear penetration depth becomes larger than the London
penetration depth.
