https://doi.org/10.1140/epjc/s10052-022-10853-5
Regular Article - Theoretical Physics
Hydrodynamic representation and energy balance for Dirac and Weyl fermions in curved space-times
1
Departamento de Física, Centro de Investigación y de Estudios Avanzados del IPN, A.P. 14-740, 07000, Mexico City, Mexico
2
Laboratoire de Physique Théorique, Université de Toulouse, CNRS, UPS, Toulouse, France
Received:
26
July
2022
Accepted:
26
September
2022
Published online:
11
October
2022
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.
© The Author(s) 2022
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