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Title: Lagrangian geometrical optics of nonadiabatic vector waves and spin particles

Linear vector waves, both quantum and classical, experience polarization-driven bending of ray trajectories and polarization dynamics that can be interpreted as the precession of the "wave spin". Here, both phenomena are governed by an effective gauge Hamiltonian vanishing in leading-order geometrical optics. This gauge Hamiltonian can be recognized as a generalization of the Stern-Gerlach Hamiltonian that is commonly known for spin-1/2 quantum particles. The corresponding reduced Lagrangians for continuous nondissipative waves and their geometrical-optics rays are derived from the fundamental wave Lagrangian. The resulting Euler-Lagrange equations can describe simultaneous interactions of N resonant modes, where N is arbitrary, and lead to equations for the wave spin, which happens to be an (N2 - 1)-dimensional spin vector. As a special case, classical equations for a Dirac particle (N = 2) are deduced formally, without introducing additional postulates or interpretations, from the Dirac quantum Lagrangian with the Pauli term. The model reproduces the Bargmann-Michel-Telegdi equations with added Stern-Gerlach force.
 [1] ;  [1]
  1. Princeton Univ., Princeton, NJ (United States). Dept. of Astrophysical Sciences
Publication Date:
OSTI Identifier:
Report Number(s):
Journal ID: ISSN 0375-9601; PII: S0375960115006404
Grant/Contract Number:
DE274-FG52-08NA28553; AC02-09CH11466; FA9550-11-C-0028
Accepted Manuscript
Journal Name:
Physics Letters. A
Additional Journal Information:
Journal Volume: 379; Journal Issue: 38; Journal ID: ISSN 0375-9601
Research Org:
Princeton Plasma Physics Laboratory (PPPL), Princeton, NJ (United States)
Sponsoring Org:
Country of Publication:
United States
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS anomalous magnetic-moment; dirac-equation; electromagnetic-field; inhomogeneous-medium; mode conversion; precession; electron; polarization; light; limit