On photon angular momentum: transversality condition, Berry degree of freedom, and non-commutativity of photon position

TL;DR

This paper explores the quantum structure of photon angular momentum, revealing the roles of the transversality condition, Berry potential, and intrinsic reference system in understanding photon spin, orbital angular momentum, and related quantum effects.

Contribution

It introduces the concept of the Berry degree of freedom and the intrinsic reference system to clarify photon angular momentum and its non-commutative properties, challenging traditional views.

Findings

Photon orbital and spin angular momenta do not satisfy standard commutation relations.

The helicity is the only intrinsic degree of freedom for the photon.

The intrinsic reference system explains the spin Hall effect of light.

Abstract

Different from the usual conclusion that the separation of the photon angular momentum into orbital and spin parts is physically meaningless, the orbital and spin angular momenta are demonstrated in the first-quantization framework not to satisfy the standard commutation relation. It is shown on the basis of the transversality condition that the spin is aligned with the propagation direction so that only the helicity can be the intrinsic degree of freedom. It is also shown on the same basis that only in the so-called intrinsic reference system does the helicity behave intrinsic. The intrinsic reference system of the photon is determined by the "action" of a gauge potential, the Berry potential, on the helicity of the photon. The Berry potential is fixed by a vector-valued degree of freedom, called the Berry degree of freedom. Because only the position of the photon in its intrinsic reference system is canonically conjugate to the momentum, the intrinsic reference system itself is endowed with quantum effects that depend on the Berry degree of freedom as well as the helicity. This not only explains the so-called spin Hall effect of light but also helps to understand why the total angular momentum cannot be generally split into helicity-independent orbital and helicity-dependent spin parts.