Anomalous Non-Conservation Of Fermionic Charge

Abstract

AbstractThis chapter opens the discussion of physical phenomena in the vacuum with Fermi points. The non-trivial topology in the momentum space leads to anomalies produced by the massless chiral fermions in the presence of collective fields such as magnetic field, textures, and vortices. In 3He-A, this gives rise to the anomalous mass current, the paradox of the orbital angular momentum, etc. All these phenomena are of the same origin as the chiral anomaly in relativistic quantum field theories. For example, the momentum exchange between superfluid vacuum and quasiparticles in 3He-A is analogous to electroweak baryoproduction — formation of excess of matter over anti-matter due to chiral anomaly. This allowed for the measurement of the spectral-flow force acting on a vortex-skyrmion in superfluid in 3He-A to experimentally verify the Adler–Bell–Jackiw equation describing chiral anomaly in particle physics. The chapter also discusses the Novikov–Wess–Zumino action, the interplay between r-space and p-space topology relevant for the discussed phenomena, and introduces 3 reactive forces acting on a vortex in fermionic superfluids: Magnus, Iordanskii, and Kopnin forces.