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Motivated by recent experimental results, we reconsider the theory of the edge excitations for the fractional Hall effect at filling factors $\nu=p/(2np+1)$. We propose to modify the standard $u(1)\otimes su(p)$ edge theory for this series by introducing twist fields which change the boundary conditions of the bosonic fields and simulate the effect of fractions of flux quanta $\phi_0/p$. This has the effect of removing the conserved charges associated to the neutral modes while keeping the right statistics of the particles. The Green function of the electron in presence of twists decays at long distance with an exponent varying continuously with $\nu$.

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.

The quantum theory of fields is largely based on studying perturbations around non-interacting, or free, field theories, which correspond to a collection of quantum-mechanical harmonic oscillators. The quantum theory of an ordinary fluid is `freer', in the sense that the non-interacting theory also contains an infinite collection of quantum-mechanical free particles, corresponding to vortex modes. By computing a variety of correlation functions at tree- and loop-level, we give evidence that a quantum perfect fluid can be consistently formulated as a low-energy, effective field theory. We speculate that the quantum behaviour is radically different to both classical fluids and quantum fields, with interesting physical consequences for fluids in the low temperature regime.

The quantum theory of fields is largely based on studying perturbations around non-interacting, or free, field theories, which correspond to a collection of quantum-mechanical harmonic oscillators. The quantum theory of an ordinary fluid is `freer', in the sense that the non-interacting theory also contains an infinite collection of quantum-mechanical free particles, corresponding to vortex modes. By computing a variety of correlation functions at tree- and loop-level, we give evidence that a quantum perfect fluid can be consistently formulated as a low-energy, effective field theory. We speculate that the quantum behaviour is radically different to both classical fluids and quantum fields, with interesting physical consequences for fluids in the low temperature regime.