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 -- volume preserving 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 to 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 Girvin-MacDonald-Platzman algebra to (3+1)-dimensional spacetime by the inclusion of the vortex-density 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 ${\mathbb{Z}}_2^{}$ topological insulators in three-dimensional space.

12 pages, 1 figure

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• Classification of topological insulators and superconductors in three spatial dimensions
• Topological Field Theory of Time-Reversal Invariant Insulators
• Physics of three dimensional bosonic topological insulators: Surface Deconfined Criticality and Quantized Magnetoelectric Effect
• D-Algebra Structure of Topological Insulators
• Magnetic translation algebra with or without magnetic field in the continuum or on arbitrary Bravais lattices in any dimension

Cited by in corpus (1)

• Theory of the fractional quantum Hall effect in Weyl semimetals