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Research Article Open access CC BY 4.0

The Quantum Hydrodynamic Formulation of Dirac Equation and Its Generalized Stochastic and Non-linear Analogs

Piero Chiarelli

Physical Science International Journal · pp. 93–114 · Published 6 Nov 2014

10.9734/PSIJ/2015/12534

Abstract

The quantum hydrodynamic-like equations as a function of two real sets of variables (i.e., the 4x4 action matrix and the 4-dimensional wave function modulus vector) of the Dirac equation are derived in the present work.  The paper shows that in the low velocity limit the equations lead to the hydrodynamic representation of the Pauli’s equation for charged particle with spin given by Janossy [1] and by Bialynicki et al [2]. The Lorentz invariance of the relativistic quantum potential that generates the non-local behavior of the quantum mechanics is discussed.  

Quantum hydrodynamic analogy relativistic quantum hydrodynamic analogy hydrodynamic form of Dirac equation stochastic Dirac equation non-linear Dirac equation

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Cited by 4

The symplectic geometrical formulation of quantum hydrodynamics

Andika Kusuma Wijaya, Arief Hermanto, Muhammad Farchani Rosyid · International Journal of Geometric Methods in Modern Physics · 2022

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