Topological BF theory of the quantum hydrodynamics of incompressible polar fluids
Abstract
We analyze a hydrodynamical model of a polar fluid in (3 + 1)dimensional spacetime. We explore a spacetime symmetry (volumepreserving diffeomorphisms) to construct an effective description of this fluid in terms of a topological BF theory. The two degrees of freedom of the BF theory are associated with the mass (charge) flows of the fluid and its polarization vorticities. We discuss the quantization of this hydrodynamic theory, which generically allows for fractionalized excitations. We propose an extension of the GirvinMacDonaldPlatzman algebra to (3 + 1)dimensional spacetime by the inclusion of the vortexdensity operator in addition to the usual charge density operator and show that the same algebra is obeyed by massive Dirac fermions that represent the bulk of Z_{2} topological insulators in threedimensional space.
 Publication:

Physical Review B
 Pub Date:
 December 2014
 DOI:
 10.1103/PhysRevB.90.235118
 arXiv:
 arXiv:1408.5417
 Bibcode:
 2014PhRvB..90w5118T
 Keywords:

 73.43.f;
 73.23.b;
 73.20.At;
 Quantum Hall effects;
 Electronic transport in mesoscopic systems;
 Surface states band structure electron density of states;
 Condensed Matter  Mesoscale and Nanoscale Physics;
 Condensed Matter  Strongly Correlated Electrons
 EPrint:
 12 pages, 1 figure