Madelung Structure of the Dirac Equation

Abstract

We consider the Dirac equations in polar form proving that they can equivalently be re-configured into a system of equations consisting of derivatives of the velocity density plus the Hamilton-Jacobi equation, giving the momentum in terms of relativistic quantum potentials (i.e. displaying first-order derivatives of the two degrees of freedom of the spinor field): this system is said to have Madelung structure. Conservation laws, second-order equations and multi-valuedness are also discussed.

11 pages

References in corpus (10)

• Axial-Vector Torsion and the Teleparallel Kerr Spacetime
• Covariant Inertial Forces for Spinors
• The Madelung Picture as a Foundation of Geometric Quantum Theory
• Towards a mathematical Theory of the Madelung Equations
• Dirac Theory in Hydrodynamic Form
• Generalized Rate Operator Quantum Jumps via Realization-Dependent Transformations
• Dirac hydrodynamics in 19 forms
• General-relativistic wave$-$particle duality with torsion
• Classical characters of spinor fields in torsion gravity
• Euler and Pontryagin currents of the Dirac operator

Cited by in corpus (1)

• A solution of the quantum time of arrival problem via mathematical probability theory