Classical and quantum theories of spin

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.

11 pages, Latex, to be published in Found. Phys

References in corpus (3)

• Some remarks about intrinsic parity in Ryder's derivation of the Dirac equation
• Proper time derivatives in quantum mechanics
• Feynman's proper time approach to QED

Cited by in corpus (8)

• Lagrangian geometrical optics of nonadiabatic vector waves and spin particles
• On the correspondence between quantum and classical variational principles
• Interaction Vertex for Classical Spinning Particles
• Feynman's proper time approach to QED
• Curved-spacetime dynamics of spin-$\frac{1}{2}$ particles in superposed states from a WKB approximation of the Dirac equation
• On the discovery of the classical equations for spin motion in electromagnetic field
• The Logic behind Feynman's Paths
• Dynamics of charged spin-$\frac{1}{2}$ particles in superposed states minimally coupled to electromagnetism in curved spacetime within the WKB approximation