Photons in a Ball

TL;DR

This paper analyzes the quantum electromagnetic field inside a large spherical cavity with stationary charges, revealing the ground state of physical photons as a coherent state with occupation numbers related to total charge.

Contribution

It introduces a gauge-invariant infra-red regularization method using a spherical cavity and characterizes the quantum ground state of photons in this setting as a coherent state.

Findings

Ground state of photons is a coherent state with a mean occupation number proportional to total charge squared.

Electric field state is a minimum uncertainty coherent state due to Gauss law constraints.

Results confirm previous formulas derived using a finite photon mass for infra-red regularization.

Abstract

The electromagnetic field inside a spherical cavity of large radius R is considered in the presence of stationary charge and current densities. R provides infra-red regularization while maintaining gauge invariance. The quantum ground state of physical photons forming the magnetic field is found to be a coherent state with a definite mean occupation number. The electric field, which is determined by the Gauss law constraint, is maintained by a minimum uncertainty coherent state, according to the projection operator approach to the quantization of constrained systems. The mean occupation number of this state is proportional to the square of the total charge. The results confirm formulae obtained previously from a calculation with a finite photon mass for infra-red regularization.