The role of the Riemann-Silberstein vector in classical and quantum theories of electromagnetism

TL;DR

The paper reviews how the Riemann-Silberstein vector simplifies electromagnetic theory in classical and quantum physics, highlighting its advantages in derivations and its potential as an optimal photon wave function.

Contribution

It demonstrates the utility of the Riemann-Silberstein vector in simplifying electromagnetic descriptions and advocates for its use as the best photon wave function.

Findings

RS vector simplifies classical electromagnetic equations

RS vector makes quantum electromagnetic derivations more transparent

RS vector is a strong candidate for the photon wave function

Abstract

It is shown that the use of the Riemann-Silberstein (RS) vector greatly simplifies the description of the electromagnetic field both in the classical domain and in the quantum domain. In this review we describe many specific examples where this vector enables one to significantly shorten the derivations and make them more transparent. We also argue why the RS vector may be considered as the best possible choice for the photon wave function.