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

• Main Authors: Yaakov Friedman, David Hai Gootvilig, Tzvi Scarr
• Format: Article
• Language: English
• Published: MDPI AG 2019-11-01
• Series: Symmetry
• Subjects: retarded potential; whittaker scalar potential; pre-potential; lorentz invariance; spin-half representation; self-dual field
• Online Access: https://www.mdpi.com/2073-8994/11/12/1430
• ISSN: 2073-8994

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.