The Pre-Potential of a Field Propagating with the Speed of Light and Its Dual Symmetry

Relativity theory assumes that force fields propagate with the speed of light. We show that such force fields generated by a single source can be described by a pre-potential, which is a complex-valued function on spacetime outside the worldline of the source. The pre-potential is invariant under a...

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Bibliographic Details
Published in:Symmetry (Basel) 2019-12, Vol.11 (12), p.1430
Main Authors: Friedman, Yaakov, Gootvilig, David Hai, Scarr, Tzvi
Format: Article
Language:English
Subjects:
Dimensional analysis
Electromagnetic fields
Electromagnetism
Light
Light speed
lorentz invariance
Mathematical functions
pre-potential
Quantum field theory
Relativity
retarded potential
self-dual field
Spacetime
spin-half representation
Symmetry
Velocity
Wave equations
whittaker scalar potential
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Summary:Relativity theory assumes that force fields propagate with the speed of light. We show that such force fields generated by a single source can be described by a pre-potential, which is a complex-valued function on spacetime outside the worldline of the source. The pre-potential is invariant under a spin-half representation of the Lorentz group acting on complexified spacetime. The complex four-potential of such a field is defined and calculated explicitly from the pre-potential without assuming any particular force law for the field. The real part of the obtained four-potential coincides with the known Liénard–Wiechert potential. The symmetry of the four-potential is described herein. The pre-potential satisfies the wave equation. The single source electromagnetic field derived from this four-potential is self-dual or anti-self-dual. The pre-potential and the four-potential are extended to a field with several sources.
ISSN:2073-8994
2073-8994
DOI:10.3390/sym11121430