Michael Ibison
Electromagnetic Foundation of Dirac Theory
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ABSTRACT. The dynamics of classical charges subject to a particular variant of electromagnetic direct particle interaction are shown to derive from a homogeneous differential equation in a Clifford Multivector. Under appropriate conditions the multivector can be 'factorized' to give a Dirac Equation whose bi-spinor operands are eigenvectors of the multivector, thereby giving an electromagnetic basis for the Dirac Equation.
The Clifford multivector is an ensemble of vector and bi-vector contributions from the potential and Faraday of the auxiliary ( adjunct ) fields of direct particle interaction, each member generated by a unique current. The presumption of light-speed motion of the charge generates non-linear constraints on these fields that preclude their super-position in the traditional sense. Representation invariance (e.g. Fourier-space versus real space) inherent in a linear differential system survives unaffected however. These conditions are shown to be responsible for the otherwise enigmatic eigenvalue selection / wavefunction collapse behavior characteristic of Dirac bi-spinors.
Though time-symmetric adjunct fields are intrinsic to the direct action paradigm, their elimination has been the main focus of works in that field - notably by Wheeler and Feynman - in an attempt to make direct particle interaction conform to Maxwell field theory. By contrast, in this work time-symmetric fields are the foundation of Dirac bi-spinors. Accidentally we also find a novel explanation of the emergence of exclusively retarded radiation from the direct action paradigm that makes no appeal to special boundary conditions.