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

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## Abstract

**:**

## 1. Introduction and Motivation

## 2. Pre-Potential and Four-Potential of a Field Generated by a Single Source

#### 2.1. Definition of the Pre-Potential of a Field Generated by a Single Source

**Definition**

**1.**

**Definition**

**2.**

#### 2.2. Matrix Representations of Spacetime

#### 2.3. Lorentz Group Representations of ${M}_{c}$

**Definition**

**3.**

**Definition**

**4.**

#### 2.4. Lorentz Invariance of the Pre-Potential and the Conjugation

**Claim**

**1.**

**Claim**

**2.**

#### 2.5. The Four-Potential of a Moving Source

**Definition**

**5.**

#### 2.6. The Symmetry of the Complex Four-Potential

**Claim**

**3.**

**Claim**

**4.**

#### 2.7. The Pre-Potential and the Wave Equation

**Claim**

**5.**

## 3. The Electromagnetic Field Tensor of a Moving Source and Its Self-Duality

**Claim**

**6.**

## 4. Discussion

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**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.
https://doi.org/10.3390/sym11121430

**AMA Style**

Friedman Y, Gootvilig DH, Scarr T.
The Pre-Potential of a Field Propagating with the Speed of Light and Its Dual Symmetry. *Symmetry*. 2019; 11(12):1430.
https://doi.org/10.3390/sym11121430

**Chicago/Turabian Style**

Friedman, Yaakov, David Hai Gootvilig, and Tzvi Scarr.
2019. "The Pre-Potential of a Field Propagating with the Speed of Light and Its Dual Symmetry" *Symmetry* 11, no. 12: 1430.
https://doi.org/10.3390/sym11121430