Hydrodynamic action for orbital and superfluid dynamics of 3He-A at T = O

The anomaly in the dynamics of the orbital vector l in superfluid 3He-A, which corresponds to the chiral anomaly and zero-charge effect in 3 + 1 quantum field theory (QFT) with chiral fermions, is considered in the presence of superflow. The hydrodynamic action which describes the dynamics of both the l vector and the superfluid velocity Vs field, is derived at T=0 in the collisionless limit using the fact that in the vicinity of the gap nodes the Bogoliubov quasiparticles behave as chiral relativistic fermions. While the quantity B=kFl plays the part of the vector potential of the effective electromagnetic field acting on the chiral fermions, the combination B4=kF(vsl) corresponds to the scalar component of th electromagnetic field. As a result the vs field contributes to the Wess-Zumino term in the action which is responsible for the chiral anomaly. In the collisionless limit the hydrodynamic momentum is conserved but is not well-defined because of the chiral anomaly: due to the flow of the quasiparticle energy levels through the gap nodes during the dynamics of l, the linear momentum of the liquid depends on the prehistory of the l field and therefore cannot be expressed in terms of the instantaneous values of l and vs. In the opposite limit the quasiparticle scattering on the container wall becomes important. As a result the quasiparticles which fill the energy levels crossing the gap nodes are removed from the coherent motion of liquid and their linear momentum transfer to the walls at a rate dictated by the level flow process. In this limit the linear momentum is well defined in terms of l and vs but is not conserved. This nonconservation of the hydrodynamic linear momentum is analogous to the nonconservation of the chiral charge in QFT with chiral anomaly. It leads to an additional force acting on the moving quantized vortices, which resembled the Iordanskii force. 10 refs