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The Dirac–Hestenes Equation and its Relation with the Relativistic de Broglie–Bohm Theory

Antônio M. Moya, Waldyr A. Rodrigues, Samuel A. Wainer

arXiv:1610.09655Advances in Applied Clifford AlgebrasApr 4, 20173 citations

The Dirac equation in the de Broglie-Bohm theory

D. Ranganathan

Physics Letters AMar 1, 19881 citation

The Dirac equation in the de Broglie-Bohm theory of motion

Peter Holland

Foundations of PhysicsOct 1, 199225 citations

Relativistic and Newton–Cartan particle in de Broglie–Bohm theory

Josef Klusoň

This paper is devoted to the analysis of massive particle in general and Newton–Cartan Background in de Broglie–Bohm theory. We find classical and quantum version of Hamilton–Jacobi equations and their relations to wave equations. We also discuss fundamental difference between classical and quantum description of these two systems.

arXiv:1807.02310Modern Physics Letters AJan 16, 20190 citations

Quantum Abraham models with de Broglie-Bohm laws of electron motion

Michael K.‐H. Kiessling

We discuss a class of quantum Abraham models in which the N‐particle spinor wave function of N electrons solves a Pauli respectively Schrödinger equation, featuring regularized classical electromagnetic potentials which solve the semi‐relativistic Maxwell‐Lorentz equations for regularized point charges, which move according to some de Broglie‐Bohm law of quantum motion. Thus there is a feedback loop from the actual particle motions to the wave function. The electrons have a bare charge and positive bare mass different from their empirical charge and mass due to renormalization by the self‐fields. In the classical limit the various models reduce to the Hamilton‐Jacobi version of corresponding Abraham models of classical electron theory.We discuss a class of quantum Abraham models in which the N‐particle spinor wave function of N electrons solves a Pauli respectively Schrödinger equation, featuring regularized classical electromagnetic potentials which solve the semi‐relativistic Maxwell‐Lorentz equations for regularized point charges, which move according to some de Broglie‐Bohm law of quantum motion. Thus there is a feedback loop from the actual particle motions to the wave function. The electrons have a bare charge and positive bare mass different from their empirical charge and mass due to renormalization by the self‐fields. In the classical limit the various models reduce to the Hamilton‐Jacobi version of corresponding Abraham models of classical electron theory.

AIP conference proceedingsJan 1, 20066 citations

Clifford Algebras and the Dirac-Bohm Quantum Hamilton-Jacobi Equation

Basil J. Hiley, R. E. Callaghan

Foundations of PhysicsMay 19, 201145 citations

The Relativistic Hamilton–Jacobi Equation for a Massive, Charged and Spinning Particle, its Equivalent Dirac Equation and the de Broglie–Bohm Theory

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The Relativistic Hamilton–Jacobi Equation for a Massive, Charged and Spinning Particle, its Equivalent Dirac Equation and the de Broglie–Bohm Theory

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