Four no-go theorems on the existence of spin and orbital angular momentum of massless bosons

TL;DR

This paper proves four fundamental theorems demonstrating the impossibility of decomposing the total angular momentum of massless bosons, like photons, into separate spin and orbital components, challenging common assumptions in light's angular momentum studies.

Contribution

It establishes four no-go theorems showing the fundamental impossibility of splitting angular momentum of massless bosons into spin and orbital parts, even under generalized conditions.

Findings

No legitimate spin and orbital angular momentum splitting for photons.

Splitting is impossible even if operators generate non-internal or non-SO(3) symmetries.

Results challenge existing approaches to light's angular momentum decomposition.

Abstract

The past decades have seen substantial interest in the so-called orbital angular momentum (OAM) of light, driven largely by its diverse range of applications. However, there are fundamental theoretical issues with decomposing the angular momentum of massless particles, such as photons, into spin (SAM) and orbital angular momentum parts. While the angular momentum of massive particles has a natural splitting into the Wigner SAM and OAM, there are numerous proposed splittings for photons and no consensus about which is correct. Moreover, it has been shown that most of the proposed SAM and OAM operators do not satisfy the defining commutation relations of angular momentum operators and are thus not legitimate splittings. Here, we prove that it is generally impossible to split the total angular momentum operator of massless bosons, such as photons and gravitons, into spin and orbital parts. We prove two further generalizations of this result, showing that there are no SAM-OAM splittings even if (1) the SAM operator generates non-internal symmetries or (2) if one allows the SAM and OAM operators to generate non-SO(3) symmetries.