Origin of Gauge Theories in Electrodynamics

- Jay Solanki

## Abstract

The potential formulation has significant advantages over field
formulation in solving complicated problems in electromagnetic field
theory. One essential part of electromagnetic field theory's potential
formulation is gauge invariance and gauge theories because it provides
an extra degree of freedom. By using this extra degree of freedom, we
can solve complicated electromagnetic problems quickly. Thus, it is
necessary to include a systematic explanation of gauge theories in
teaching electromagnetic theory. However, textbooks usually formulate
gauge theories by using Maxwell's equations of electromagnetism, by
using vector calculus identities. However, this method of formulation of
gauge theories does not give a clear idea about the origin of gauge
theories and gauge invariance in electromagnetism. Here the author
formulates gauge theories from wave equations of the electric and
magnetic fields instead of directly using Maxwell's equations. This
method generalizes all gauge theories like Lorenz gauge theory, Coulomb
gauge theory, Etc. Gauge theory, because of the way the author derives
it, gives a distinct idea about the mathematical origin of the gauge
theories and gauge invariance in electromagnetic field theory. Thus, the
author reviews the origin of gauge theories in electromagnetic field
theory and develops a distinct and effective method to introduce gauge
theory in the teaching of electromagnetic field theory that can provide
better understanding of the topic to undergraduate students.