Multipole expansions in quantum radiation theory

TL;DR

This paper derives a multipole expansion for quantum spontaneous radiation amplitudes using irreducible tensor techniques, enabling detailed analysis of electromagnetic interactions in quantum systems.

Contribution

It introduces a new multipole expansion method for quantum radiation amplitudes based on irreducible tensors, applicable in various electromagnetic interaction regimes.

Findings

Series represents total radiation amplitude as sum of electric and magnetic multipole contributions

Coefficients encode all information about the radiating system via current density tensors

Method applicable to both long-wave approximation and beyond

Abstract

With the help of mathematical technique of irreducible tensors the multipole expansion for the probability amplitude of spontaneous radiation of a quantum system is derived. It is shown that the found series represents the total radiation amplitude in the form of the sum of radiation amplitudes of electric and magnetis multipole photons. All information about the radiating system is contained in the coefficients of the series which are the irreducible tensors being determined by the current density of transition. The expansion can be used for solving different problems that arise in studying electromagnetic field-quantum system interaction both in long-wave approximation and outside its framework.