# Maxwell Electrodynamics in Terms of Physical Potentials

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Gauge-Invariant Physical Potentials

#### 2.1. Stationary Electromagnetism and Physical Potentials

#### 2.2. Formulation of Full Electrodynamics in Terms of Physical Potentials

## 3. Special Relativity as a Symmetry of Maxwell’s Equations

#### 3.1. Manifest Lorentz Symmetry

#### 3.2. Closing the Circle: Physical Vector Potentials from the Standard Formulation

#### 3.2.1. With Sources

#### 3.2.2. Without Sources

## 4. Applications of the Physical Potentials

#### 4.1. Coupling to Charged Scalar Fields

#### 4.2. Aharonov–Bohm Effect

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

- Yang, C.N. The conceptual origins of Maxwell’s equations and gauge theory. Phys. Today
**2014**, 67, 45. [Google Scholar] [CrossRef] - Einstein, A. Zur Elektrodynamik bewegter Körper. Ann. Phys.
**1905**, 17, 37, reprinted as On the Electrodynamics of Moving Bodies. In The Principle of Relativity; Dover: New York, NY, USA, 1952. [Google Scholar] [CrossRef] - Landau, L.D.; Lifschitz, E.M. Classical Theory of Fields; Pergamon Press: Oxford, UK, 1975. [Google Scholar]
- Jackson, J.D. Classical Electrodynamics; Wiley Eastern: Hoboken, NJ, USA, 1974. [Google Scholar]
- Feynman, R.P. The Feynman Lectures on Physics; Addison-Wesley Publishing Co.: Boston, MA, USA, 1963; Volume 2. [Google Scholar]
- Bhattacharjee, S.; Majumdar, P. Gauge-free Coleman-Weinberg Potential. Eur. Phys. J. C
**2013**, 73, 2348, e-Print arXiv:1302.7272. [Google Scholar] [CrossRef] - Synge, J.L. Model Universes with Spherical Symmetry. Ann. Mat. Pura Appl.
**1974**, 86, 239–255. [Google Scholar] [CrossRef] - Basu, A.; Majumdar, P.; Mitra, I. Gauge-invariant Matter Field Actions from Iterative Nöther Coupling. Phys. Rev. D
**2018**, 98, 105018, e-Print arXiv: 1711.05608. [Google Scholar] [CrossRef] - Aharonov, Y.; Bohm, D. Significance of Electromagnetic Potentials in the Quantum Theory. Phys. Rev.
**1959**, 115, 485. [Google Scholar] [CrossRef] - Itzykson, C.; Zuber, J.B. Quantum Field Theory; McGraw-Hill Inc.: New York, NY, USA, 1980. [Google Scholar]
- Srednicki, M. Quantum Field Theory; Cambridge University Press: Cambridge, UK, 2007. [Google Scholar]
- Van Holten, J.W. Aspects of BRST quantization. In Topology and Geometry in Physics; Springer: Berlin/Heidelberg, Germany, 2005. [Google Scholar]
- Bick, E.; Steffen, F.D. (Eds.) Springer Lecture Notes in Physics 659. Available online: https://www.springer.com/gp/book/9783540231257 (accessed on 10 June 2019).
- Online Lecture Notes on Quantum Field Theory by David Tong. Available online: http://www.damtp.cam.ac.uk/user/tong/qft.html (accessed on 10 June 2019).
- Synge, J.L. Point Particles and Energy Tensors in Special Relativity. Ann. Mat. Pura Appl.
**1970**, 84, 33–59. [Google Scholar] [CrossRef]

© 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Majumdar, P.; Ray, A.
Maxwell Electrodynamics in Terms of Physical Potentials. *Symmetry* **2019**, *11*, 915.
https://doi.org/10.3390/sym11070915

**AMA Style**

Majumdar P, Ray A.
Maxwell Electrodynamics in Terms of Physical Potentials. *Symmetry*. 2019; 11(7):915.
https://doi.org/10.3390/sym11070915

**Chicago/Turabian Style**

Majumdar, Parthasarathi, and Anarya Ray.
2019. "Maxwell Electrodynamics in Terms of Physical Potentials" *Symmetry* 11, no. 7: 915.
https://doi.org/10.3390/sym11070915