On the quantization of the nonintegrable phase in electrodynamics

TL;DR

This paper explores how a path-dependent formalism in gauge theory can describe flux and charge quantization, especially in the presence of magnetic monopoles, and relates fundamental charge units to the fine structure constant.

Contribution

It introduces a path-dependent formalism for gauge theories that provides a unified description of flux and charge quantization, including in monopole scenarios.

Findings

Formalism simplifies flux and charge quantization descriptions.

Demonstrates the relationship between fundamental charge and the fine structure constant.

Applies the formalism to a (1+1) dimensional model showing quantization links.

Abstract

Using the fact that the nonintegrable phase factor can reformulate the gauge theory in terms of path dependent vector potentials, the quantization condition for the nonintegrable phase is investigated. It is shown that the path-dependent formalism can provide compact description of the flux quantization and the charge quantization at the existence of a magnetic monopole. Moreover, the path-dependent formalism gives suggestions for searching of the quantized flux in different configurations and for other possible reasons of the charge quantization. As an example, the developed formalism is employed for a (1+1) dimensional world, showing the relationship between the fundamental unit of the charge and the fine structure constant for this world.