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Symmetry and Special Relativity
Open AccessArticle

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

1
Extended Relativity Research Center, Departments of Mathematics and Physics, Jerusalem College of Technology, P.O. Box 16031, Jerusalem 91160, Israel
2
Department of Physics, Jerusalem College of Technology, P.O. Box 16031, Jerusalem 91160, Israel
3
Department of Mathematics, Jerusalem College of Technology, P.O. Box 16031, Jerusalem 91160, Israel
*
Author to whom correspondence should be addressed.
Symmetry 2019, 11(12), 1430; https://doi.org/10.3390/sym11121430
Received: 10 October 2019 / Revised: 11 November 2019 / Accepted: 18 November 2019 / Published: 20 November 2019
(This article belongs to the Special Issue Relativity Based on 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 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. View Full-Text
Keywords: retarded potential; Whittaker scalar potential; pre-potential; Lorentz invariance; spin-half representation; self-dual field retarded potential; Whittaker scalar potential; pre-potential; Lorentz invariance; spin-half representation; self-dual field
MDPI and ACS Style

Friedman, Y.; Gootvilig, D.H.; Scarr, T. The Pre-Potential of a Field Propagating with the Speed of Light and Its Dual Symmetry. Symmetry 2019, 11, 1430.

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