Explicit derivation of the Pauli spin matrices from the Jones vector

TL;DR

This paper derives the Pauli spin matrices explicitly from Jones vectors using dyadic tensor representations and anti-commutation relations, providing a clear mathematical connection between polarization optics and quantum spin operators.

Contribution

It introduces a direct derivation of Pauli matrices from Jones vector formalism, bridging optics and quantum mechanics in a novel way.

Findings

Explicit derivation of Pauli matrices from Jones vectors

Establishment of tensorial relations and anti-commutation properties

Enhanced understanding of the mathematical link between optics and quantum spin

Abstract

Using dyadic representations elaborated from vectors of Jones, and calculating relations of anti-commutation of these tensorial forms, we obtain in shape explicit the Pauli spin matrices.