Relativistic spin operator must be intrinsic

TL;DR

This paper proposes that the relativistic spin operator should be intrinsic, leading to a unique, physically consistent definition that aligns with covariance and non-relativistic limits, resolving longstanding ambiguities.

Contribution

It introduces an intrinsic criterion for relativistic spin, ruling out previous three-vector proposals and establishing a unique, physically consistent spin operator based on Poincaré group representations.

Findings

The intrinsic spin operator is unique and physically consistent.

The proposed spin operator is covariant and matches non-relativistic limits.

An observer-independent model for electromagnetic-spin interaction supports the approach.

Abstract

Although there are many proposals of relativistic spin observables, there is no agreement about the adequate definition of this quantity. This problem arises from the fact that, in the present literature, there is no consensus concerning the set of properties that such an operator should satisfy. Here we present how to overcome this problem by imposing a condition that everyone should agree about the nature of the relativistic spin observable: it must be intrinsic. The intrinsicality concept is analyzed in the relativistic classical limit and then it is extended to the quantum regime, the spin problem being treated in the context of the irreducible unitary representations of the Poincar\'{e} group. This approach rules out three-vector proposals of relativistic spin observable and leads to a unique satisfactory spin definition that, besides being intrinsic, also possesses interesting physical features such as covariance and consistency of predictions in the non relativistic limit. To support the presented results from an operational perspective, a consistent observer-independent model for the electromagnetic-spin interaction is also presented.