Maxwell electromagnetic theory from a viewpoint of differential forms

TL;DR

This paper reformulates Maxwell's equations using differential forms, viewing classical electrodynamics as a curvature in gauge theory, providing a geometric perspective in both 3D and 4D frameworks.

Contribution

It introduces a differential forms approach to Maxwell's equations and interprets electrodynamics as a curvature in gauge theory, offering a unified geometric viewpoint.

Findings

Maxwell equations expressed via differential forms in 3D and 4D

Electrodynamics interpreted as curvature of a line bundle

Provides a gauge theory perspective on classical electrodynamics

Abstract

In this paper, we discuss the Maxwell equations in terms of differential forms, both in the 3-dimensional space and in the 4-dimensional space-time manifold. Further, we view the classical electrodynamics as the curvature of a line bundle, and fit it into gauge theory.