Lagrangian geometrical optics of nonadiabatic vector waves and spin particles
Linear vector waves, both quantum and classical, experience polarizationdriven 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 leadingorder geometrical optics. This gauge Hamiltonian can be recognized as a generalization of the SternGerlach Hamiltonian that is commonly known for spin1/2 quantum particles. The corresponding reduced Lagrangians for continuous nondissipative waves and their geometricaloptics rays are derived from the fundamental wave Lagrangian. The resulting EulerLagrange 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 (N ^{2}  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 BargmannMichelTelegdi equations with added SternGerlach force.
 Authors:

^{[1]}
;
^{[1]}
 Princeton Univ., Princeton, NJ (United States). Dept. of Astrophysical Sciences
 Publication Date:
 Report Number(s):
 PPPL5144
Journal ID: ISSN 03759601; PII: S0375960115006404
 Grant/Contract Number:
 DE274FG5208NA28553; AC0209CH11466; FA955011C0028
 Type:
 Accepted Manuscript
 Journal Name:
 Physics Letters. A
 Additional Journal Information:
 Journal Volume: 379; Journal Issue: 38; Journal ID: ISSN 03759601
 Publisher:
 Elsevier
 Research Org:
 Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States)
 Sponsoring Org:
 USDOE
 Country of Publication:
 United States
 Language:
 English
 Subject:
 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; anomalous magneticmoment; diracequation; electromagneticfield; inhomogeneousmedium; mode conversion; precession; electron; polarization; light; limit
 OSTI Identifier:
 1256634
 Alternate Identifier(s):
 OSTI ID: 1347252
Ruiz, D. E., and Dodin, I. Y.. Lagrangian geometrical optics of nonadiabatic vector waves and spin particles. United States: N. p.,
Web. doi:10.1016/j.physleta.2015.07.038.
Ruiz, D. E., & Dodin, I. Y.. Lagrangian geometrical optics of nonadiabatic vector waves and spin particles. United States. doi:10.1016/j.physleta.2015.07.038.
Ruiz, D. E., and Dodin, I. Y.. 2015.
"Lagrangian geometrical optics of nonadiabatic vector waves and spin particles". United States.
doi:10.1016/j.physleta.2015.07.038. https://www.osti.gov/servlets/purl/1256634.
@article{osti_1256634,
title = {Lagrangian geometrical optics of nonadiabatic vector waves and spin particles},
author = {Ruiz, D. E. and Dodin, I. Y.},
abstractNote = {Linear vector waves, both quantum and classical, experience polarizationdriven 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 leadingorder geometrical optics. This gauge Hamiltonian can be recognized as a generalization of the SternGerlach Hamiltonian that is commonly known for spin1/2 quantum particles. The corresponding reduced Lagrangians for continuous nondissipative waves and their geometricaloptics rays are derived from the fundamental wave Lagrangian. The resulting EulerLagrange 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 BargmannMichelTelegdi equations with added SternGerlach force.},
doi = {10.1016/j.physleta.2015.07.038},
journal = {Physics Letters. A},
number = 38,
volume = 379,
place = {United States},
year = {2015},
month = {7}
}