Lagrangian geometrical optics of nonadiabatic vector waves and spin particles
Abstract
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.
- Authors:
-
- Princeton Univ., Princeton, NJ (United States). Dept. of Astrophysical Sciences
- Publication Date:
- Research Org.:
- Princeton Plasma Physics Laboratory (PPPL), Princeton, NJ (United States)
- Sponsoring Org.:
- USDOE
- OSTI Identifier:
- 1256634
- Alternate Identifier(s):
- OSTI ID: 1347252
- Report Number(s):
- PPPL-5144
Journal ID: ISSN 0375-9601; PII: S0375960115006404
- Grant/Contract Number:
- DE274-FG52-08NA28553; AC02-09CH11466; FA9550-11-C-0028
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Physics Letters. A
- Additional Journal Information:
- Journal Volume: 379; Journal Issue: 38; Journal ID: ISSN 0375-9601
- Publisher:
- Elsevier
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; anomalous magnetic-moment; dirac-equation; electromagnetic-field; inhomogeneous-medium; mode conversion; precession; electron; polarization; light; limit
Citation Formats
Ruiz, D. E., and Dodin, I. Y. Lagrangian geometrical optics of nonadiabatic vector waves and spin particles. United States: N. p., 2015.
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. https://doi.org/10.1016/j.physleta.2015.07.038
Ruiz, D. E., and Dodin, I. Y. Wed .
"Lagrangian geometrical optics of nonadiabatic vector waves and spin particles". United States. https://doi.org/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 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.},
doi = {10.1016/j.physleta.2015.07.038},
journal = {Physics Letters. A},
number = 38,
volume = 379,
place = {United States},
year = {Wed Jul 29 00:00:00 EDT 2015},
month = {Wed Jul 29 00:00:00 EDT 2015}
}
Web of Science
Works referenced in this record:
Axiomatic geometrical optics, Abraham-Minkowski controversy, and photon properties derived classically
journal, November 2012
- Dodin, I. Y.; Fisch, N. J.
- Physical Review A, Vol. 86, Issue 5
Gravitational Radiation in the Limit of High Frequency. I. The Linear Approximation and Geometrical Optics
journal, February 1968
- Isaacson, Richard A.
- Physical Review, Vol. 166, Issue 5
Geometric phases in the asymptotic theory of coupled wave equations
journal, October 1991
- Littlejohn, Robert G.; Flynn, William G.
- Physical Review A, Vol. 44, Issue 8
Spin-orbit interaction of a photon in an inhomogeneous medium
journal, October 1992
- Liberman, V. S.; Zel’dovich, B. Ya.
- Physical Review A, Vol. 46, Issue 8
Hall Effect of Light
journal, August 2004
- Onoda, Masaru; Murakami, Shuichi; Nagaosa, Naoto
- Physical Review Letters, Vol. 93, Issue 8
Geometrodynamics of spinning light
journal, November 2008
- Bliokh, Konstantin Y.; Niv, Avi; Kleiner, Vladimir
- Nature Photonics, Vol. 2, Issue 12
Berry phase, Lorentz covariance, and anomalous velocity for Dirac and Weyl particles
journal, January 2015
- Stone, Michael; Dwivedi, Vatsal; Zhou, Tianci
- Physical Review D, Vol. 91, Issue 2
Gauge Field Optics with Anisotropic Media
journal, March 2015
- Liu, Fu; Li, Jensen
- Physical Review Letters, Vol. 114, Issue 10
Stokes-vector evolution in a weakly anisotropic inhomogeneous medium
journal, January 2007
- Kravtsov, Yu. A.; Bieg, B.; Bliokh, K. Yu.
- Journal of the Optical Society of America A, Vol. 24, Issue 10
Non-Abelian evolution of electromagnetic waves in a weakly anisotropic inhomogeneous medium
journal, May 2007
- Bliokh, K. Yu.; Frolov, D. Yu.; Kravtsov, Yu. A.
- Physical Review A, Vol. 75, Issue 5
Polarized light in an anisotropic medium versus spin in a magnetic field [Polyarizovannyi svet v anizotropnoi srede i spin v magnitnom pole]
journal, January 1999
- Zapasskii, V. S.; Kozlov, Gleb G.
- Uspekhi Fizicheskih Nauk, Vol. 169, Issue 8
Geometric view on noneikonal waves
journal, April 2014
- Dodin, I. Y.
- Physics Letters A, Vol. 378, Issue 22-23
Classical and Quantum Theories of Spin
journal, January 1998
- Gaioli, Fabián H.; Alvarez, Edgardo T. Garcia
- Foundations of Physics, Vol. 28, Issue 10, p. 1539-1550
Modern interpretation of J.I. Frenkel's classical spin theory
journal, October 1980
- Ternov, I. M.; Bordovitsyn, V. A.
- Soviet Physics Uspekhi, Vol. 23, Issue 10
Precession of the Polarization of Particles Moving in a Homogeneous Electromagnetic Field
journal, May 1959
- Bargmann, V.; Michel, Louis; Telegdi, V. L.
- Physical Review Letters, Vol. 2, Issue 10
Asymptotic Solution of the Dirac Equation
journal, September 1963
- Rubinow, S. I.; Keller, Joseph B.
- Physical Review, Vol. 131, Issue 6
Semiclassical Limit of the Dirac Equation and Spin Precession
journal, June 2000
- Spohn, Herbert
- Annals of Physics, Vol. 282, Issue 2
Ponderomotive Forces on Waves in Modulated Media
journal, May 2014
- Dodin, I. Y.; Fisch, N. J.
- Physical Review Letters, Vol. 112, Issue 20
Ponderomotive force due to the intrinsic spin in extended fluid and kinetic models
journal, March 2011
- Stefan, Martin; Zamanian, Jens; Brodin, Gert
- Physical Review E, Vol. 83, Issue 3
Spin Contribution to the Ponderomotive Force in a Plasma
journal, September 2010
- Brodin, G.; Misra, A. P.; Marklund, M.
- Physical Review Letters, Vol. 105, Issue 10
Analytical solutions of the Dirac and the Klein-Gordon equations in plasma induced by high-intensity laser
journal, August 2013
- Raicher, Erez; Eliezer, Shalom
- Physical Review A, Vol. 88, Issue 2
The Lagrangian formulation of strong-field quantum electrodynamics in a plasma
journal, May 2014
- Raicher, Erez; Eliezer, Shalom; Zigler, Arie
- Physics of Plasmas, Vol. 21, Issue 5
Controlling the Flow of Light Using the Inhomogeneous Effective Gauge Field that Emerges from Dynamic Modulation
journal, November 2013
- Fang, Kejie; Fan, Shanhui
- Physical Review Letters, Vol. 111, Issue 20
Colloquium : Artificial gauge potentials for neutral atoms
journal, November 2011
- Dalibard, Jean; Gerbier, Fabrice; Juzeliūnas, Gediminas
- Reviews of Modern Physics, Vol. 83, Issue 4
Group Velocity and Nonlinear Dispersive Wave Propagation
journal, March 1973
- Hayes, W. D.
- Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 332, Issue 1589
I. The kinematics of an electron with an axis
journal, January 1927
- Thomas, L. H.
- The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, Vol. 3, Issue 13
The Vector Representation of Spinning Particle in the Quantum Theory, I
journal, October 1955
- Takabayasi, Takehiko
- Progress of Theoretical Physics, Vol. 14, Issue 4
On the Dirac equation with anomalous magnetic moment term and a plane electromagnetic field
journal, November 1993
- Salamin, Y. I.
- Journal of Physics A: Mathematical and General, Vol. 26, Issue 21
Classical Model of the Dirac Electron
journal, June 1984
- Barut, A. O.; Zanghi, Nino
- Physical Review Letters, Vol. 52, Issue 23
Covariant generalization of the Zitterbewegung of the electron and its SO(4,2) and SO(3,2) internal algebras
journal, March 1985
- Barut, A. O.; Thacker, W.
- Physical Review D, Vol. 31, Issue 6
The classical relativistic two-body problem with spin and self-interactions
journal, April 1990
- Barut, A. O.; Onem, C.; Unal, N.
- Journal of Physics A: Mathematical and General, Vol. 23, Issue 7
Classical relativistic spinning particle with anomalous magnetic moment: the precession of spin
journal, November 1993
- Barut, A. O.; Cruz, M. G.
- Journal of Physics A: Mathematical and General, Vol. 26, Issue 22
On the Dirac Theory of Spin 1/2 Particles and Its Non-Relativistic Limit
journal, April 1950
- Foldy, Leslie L.; Wouthuysen, Siegfried A.
- Physical Review, Vol. 78, Issue 1
Correspondence between classical and Dirac-Pauli spinors in view of the Foldy-Wouthuysen transformation
journal, March 2014
- Chen, Tsung-Wei; Chiou, Dah-Wei
- Physical Review A, Vol. 89, Issue 3
Wavefunctions of a free electron in an external field and their application in intense field interactions. II. Relativistic treatment
journal, August 1980
- Bergou, J.; Varro, S.
- Journal of Physics A: Mathematical and General, Vol. 13, Issue 8
Phase integral theory, coupled wave equations, and mode conversion
journal, January 1992
- Littlejohn, Robert G.; Flynn, William G.
- Chaos: An Interdisciplinary Journal of Nonlinear Science, Vol. 2, Issue 1
General linear mode conversion coefficient in one dimension
journal, March 1993
- Littlejohn, Robert G.; Flynn, William G.
- Physical Review Letters, Vol. 70, Issue 12
Ray-based methods in multidimensional linear wave conversion
journal, May 2003
- Tracy, Eugene R.; Kaufman, Allan N.; Brizard, Alain J.
- Physics of Plasmas, Vol. 10, Issue 5
Works referencing / citing this record:
Quasioptical modeling of wave beams with and without mode conversion. III. Numerical simulations of mode-converting beams
journal, July 2019
- Yanagihara, K.; Dodin, I. Y.; Kubo, S.
- Physics of Plasmas, Vol. 26, Issue 7
Quasioptical modeling of wave beams with and without mode conversion. II. Numerical simulations of single-mode beams
journal, July 2019
- Yanagihara, K.; Dodin, I. Y.; Kubo, S.
- Physics of Plasmas, Vol. 26, Issue 7
Quasioptical modeling of wave beams with and without mode conversion. I. Basic theory
journal, July 2019
- Dodin, I. Y.; Ruiz, D. E.; Yanagihara, K.
- Physics of Plasmas, Vol. 26, Issue 7
Extending geometrical optics: A Lagrangian theory for vector waves
journal, May 2017
- Ruiz, D. E.; Dodin, I. Y.
- Physics of Plasmas, Vol. 24, Issue 5
First-principle variational formulation of polarization effects in geometrical optics
text, January 2015
- Ruiz, D. E.; Dodin, I. Y.
- arXiv
Extending geometrical optics: A Lagrangian theory for vector waves
journal, May 2017
- Ruiz, D. E.; Dodin, I. Y.
- Physics of Plasmas, Vol. 24, Issue 5
Quasioptical modeling of wave beams with and without mode conversion. II. Numerical simulations of single-mode beams
journal, July 2019
- Yanagihara, K.; Dodin, I. Y.; Kubo, S.
- Physics of Plasmas, Vol. 26, Issue 7
Quasioptical modeling of wave beams with and without mode conversion. III. Numerical simulations of mode-converting beams
journal, July 2019
- Yanagihara, K.; Dodin, I. Y.; Kubo, S.
- Physics of Plasmas, Vol. 26, Issue 7
Massless polarized particle and Faraday rotation of light in the Schwarzschild spacetime
journal, July 2021
- Deriglazov, Alexei A.
- Physical Review D, Vol. 104, Issue 2
Relativistic ponderomotive Hamiltonian of a Dirac particle in a vacuum laser field
text, January 2015
- Ruiz, D. E.; Ellison, C. L.; Dodin, I. Y.
- arXiv
Parametric decay of plasma waves near the upper-hybrid resonance
text, January 2017
- Dodin, I. Y.; Arefiev, A. V.
- arXiv
Mode conversion in cold low-density plasma with a sheared magnetic field
text, January 2017
- Dodin, I. Y.; Ruiz, D. E.; Kubo, S.
- arXiv