The generalization of the Nelson-Halperin-Young theory of 2D melting to thedynamical 2+1D quantum case is presented. The bosonic quantum crystal dualizesin superfluids or superconductors exhibiting nematic liquid crystalline orders,corresponding with bose condensates of dislocations exhibiting a dual shearMeissner-Higgs mechanism. The topologically ordered nematic phase suggested byLammert, Toner and Rokshar finds a simple interpretation in this framework. Theordered nematic is a true quantum phase: the dynamical glide principleinterferes with the effect that the phonon spectrum of the crystal re-emergesin the direction orthogonal to the director. Novel insights follow from theduality on the fundamental nature of superfluidity and superconductivity. Thesuperfluid can be viewed as an elastic medium having lost its rigidity againstshear stresses. Upon dualizing the electrically charged crystal theelectromagnetic Meissner phase is recovered, showing peculiar screening currentoscillations when the shear penetration depth becomes larger than the Londonpenetration depth.
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