Abelian BF-Theory and Spherically Symmetric Electromagnetism

TL;DR

This paper explores three methods to quantize spherically symmetric electromagnetism by relating it to Abelian BF-theory, demonstrating their equivalence and consistency in the magnetically uncharged case.

Contribution

It introduces a novel approach by connecting spherically symmetric electromagnetism to Abelian BF-theory and compares different quantization methods.

Findings

All three quantization approaches agree in the magnetically uncharged sector.

The spherically symmetric sector is equivalent to Abelian BF-theory with boundary conditions.

The results are consistent with the general quantum symmetry reduction scheme.

Abstract

Three different methods to quantize the spherically symmetric sector of electromagnetism are presented: First, it is shown that this sector is equivalent to Abelian BF-theory in four spacetime dimensions with suitable boundary conditions. This theory, in turn, is quantized by both a reduced phase space quantization and a spin network quantization. Finally, the outcome is compared with the results obtained in the recently proposed general quantum symmetry reduction scheme. In the magnetically uncharged sector, where all three approaches apply, they all lead to the same quantum theory.