On the number and spin of photons in classical electromagnetic field

TL;DR

This paper derives a relativistically invariant expression for the photon number and total spin of classical electromagnetic fields, linking classical and quantum descriptions and revealing their interrelation through tensor quantities.

Contribution

It introduces a new invariant formula for photon number and spin in classical fields, connecting classical results with quantum operators and providing a deeper understanding of electromagnetic field properties.

Findings

Derived a relativistically invariant photon number expression.

Connected classical spin moment with quantum spin operators.

Showed the relation between photon number and spin through a tensor.

Abstract

A relativistically invariant expression for the number of photons in free classical electromagnetic field through the currents, that created the field, is derived based on the formula for the total energy--momentum of the field. It is demonstrated that it corresponds to the classical limit of the photon number operator known from the quantum electrodynamics. An expression for the total spin moment of the classical electromagnetic field is derived and it is shown that it can be interpreted in terms of spin moments of elementary photons. Similar to the total number of photons the classical spin moment is the limit of the quantum operator of the total spin. It is revealed that the total number of photons as well as the total spin moment are related to each other through a second order tensor, which can be expressed through currents that created the field.