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

Piero Chiarelli *

National Council of Research of Italy, Area of Pisa, 56124 Pisa, Moruzzi 1, Italy and Interdepartmental Center “E.Piaggio” University of Pisa, Pisa, Italy

*Author to whom correspondence should be addressed.


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.

 

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


How to Cite

Chiarelli, Piero. 2014. “The Quantum Hydrodynamic Formulation of Dirac Equation and Its Generalized Stochastic and Non-Linear Analogs”. Physical Science International Journal 5 (2):93-114. https://doi.org/10.9734/PSIJ/2015/12534.

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