Spin and Madelung fluid

Abstract

Starting from the Pauli current we obtain the decomposition of the non-relativistic local velocity in two parts: one parallel and the other orthogonal to the momentum. The former is recognized to be the ``classical'' part, that is the velocity of the center-of-mass, and the latter the ``quantum'' one, that is the velocity of the motion in the center-of-mass frame (namely, the internal ``spin motion'' or {\em Zitterbewegung}). Inserting the complete expression of the velocity into the kinetic energy term of the classical non-relativistic (i.e., Newtonian) Lagrangian, we straightforwardly derive the so-called ``quantum potential'' associated to the Madelung fluid. In such a way, the quantum mechanical behaviour of particles appears to be strictly correlated to the existence of spin and Zitterbewegung.

Cited by in corpus (11)

• Solitons of the Resonant Nonlinear Schrodinger Equation with Nontrivial Boundary Conditions and Hirota Bilinear Method
• The Madelung Picture as a Foundation of Geometric Quantum Theory
• Fundamental times, lengths and physical constants: some unknown contributions by Ettore Majorana
• Toward Local Madelung Mechanics in Spacetime
• Beyond the Relativistic Point Particle: A Reciprocally Invariant System and its Generalisation
• Deriving Spin of the Bosonic String
• Quantum-Fluid Correspondence in Relativistic Fluids with Spin: From Madelung Form to Gravitational Coupling
• Does Bohm's Quantum Force Have a Classical Origin?
• Effects of entanglement on vortex dynamics in the hydrodynamic representation of quantum mechanics
• Galilei Group with multiple central extension, vorticity and entropy generation: "Exotic" fluid in 3+1-dimensions
• A Formulation of Quantum Fluid Mechanics and Trajectories