Hydrodynamic representation and Energy Balance for Dirac and Weyl fermions in curved space-times
arXiv:2106.15803 · doi:10.1140/epjc/s10052-022-10853-5
Abstract
Using a generalized Madelung transformation, we derive the hydrodynamic representation of the Dirac equation in arbitrary curved space-times coupled to an electromagnetic field. We obtain Dirac-Euler equations for fermions involving a continuity equation and a first integral of the Bernoulli equation. Comparing between the Dirac and Klein-Gordon equations we obtain the balance equation for fermion particles. We also use the correspondence between fermions and bosons to derive the hydrodynamic representation of the Weyl equation which is a chiral form of the Dirac equation.
21 pages, accepted in EPJ C