Classical and quantum theories of spin

TL;DR

This paper reviews classical and quantum spin theories, highlighting the semiclassical limit of the Dirac equation and deriving spin precession equations, to bridge the gap between classical and quantum descriptions of spin.

Contribution

It demonstrates how the Barut-Zanghi semiclassical model emerges from the Dirac equation and compares quantum spin precession with classical theories.

Findings

The Barut-Zanghi model is derived from the Dirac equation's semiclassical limit.

Quantum spin precession equations are formulated in the Heisenberg picture.

Analogies and differences between classical and quantum spin theories are analyzed.

Abstract

A great effort has been devoted to formulate a classical relativistic theory of spin compatible with quantum relativistic wave equations. The main difficulty in order to connect classical and quantum theories rests in finding a parameter which plays the role of proper time at a purely quantum level. We present a partial review of several proposals of classical and quantum spin theories from the pioneer works of Thomas and Frenkel, revisited in the classical BMT work, to the semiclassical model of Barut and Zanghi [Phys. Rev. Lett. 52, 2009 (1984)]. We show that the last model can be obtained from a semiclassical limit of the Feynman proper time parametrization of the Dirac equation. At the quantum level we derive spin precession equations in the Heisenberg picture. Analogies and differences with respect to classical theories are discussed in detail.