Chiral waves on the Fermi-Dirac sea: Quantum superfluidity and the axial anomaly

We show that as a result of the axial anomaly, massless fermions at zero temperature define relativistic quantum superfluid. The anomaly pole implies existence gapless Chiral Density Wave (CDW), i.e. an axion-like acoustic mode irrotational and dissipationless Hamiltonian perfect fluid, is correlated fermion/anti-fermion pair excitation Fermi-Dirac sea. In D=2 dimensions chiral superfluid effective action coincides with Schwinger model e→0, CDW precisely boson. Since this identity holds also chemical potential, Dirac vacuum itself may be viewed state. collective boson U(1) phase field, which novel, non-linear realization Goldstone's theorem, extended to case symmetry breaking by anomaly. A new local form bosonic in any D even spacetime given, consistent superfluidity, its quantization shown required anomalous terms fermion current commutators. QED4 Goldstone appears triangle diagram, responsible for macroscopic non-dissipative currents Magnetic Separation Effects, well Anomalous Hall Effect. constant uniform magnetic field exact dimensional reduction from D=4 occurs e+e− propagating along direction Wave, acquires mass gap M2=e3B/2π2. Possible realizations tests theory excitations due Dirac/Weyl materials are briefly discussed.