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arXiv · 2505.05861

Madelung Structure of the Dirac Equation

Luca Fabbri
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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.

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Luca Fabbri. 2025-05-09. Madelung Structure of the Dirac Equation. https://doi.org/10.1088/1751-8121%2Fadd2b0

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