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". Both phenomena are governed by an effective gauge Hamiltonian, which vanishes 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 a $(N^2-1)$-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 Bargmann-Michel-Telegdi equations with added Stern-Gerlach force.

17 pages

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Cited by in corpus (20)

• Quasioptical modeling of wave beams with and without mode conversion: I. Basic theory
• First-principle variational formulation of polarization effects in geometrical optics
• Finite-dimensional collisionless kinetic theory
• Relativistic electron spin dynamics in a strong unipolar laser field
• Extending geometrical optics: A Lagrangian theory for vector waves
• Ponderomotive dynamics of waves in quasiperiodically modulated media
• Quasioptical modeling of wave beams with and without mode conversion: III. Numerical simulations of mode-converting beams
• Quasioptical modeling of wave beams with and without mode conversion: II. Numerical simulations of single-mode beams
• Relativistic ponderomotive Hamiltonian of a Dirac particle in a vacuum laser field
• Massless polarized particle and Faraday rotation of light in the Schwarzschild spacetime
• The Schrödinger Formalism of Electromagnetism and Other Classical Waves --- How to Make Quantum-Wave Analogies Rigorous
• Variational principles for dissipative (sub)systems, with applications to the theory of linear dispersion and geometrical optics
• Metaplectic geometrical optics for modeling caustics in uniform and nonuniform media
• On the correspondence between quantum and classical variational principles
• Metaplectic geometrical optics for ray-based modeling of caustics: Theory and algorithms
• Mode conversion in cold low-density plasma with a sheared magnetic field
• Photon topology
• Parametric decay of plasma waves near the upper-hybrid resonance
• Structure formation in turbulence as instability of effective quantum plasma
• Spin Hall effect of radiofrequency waves in magnetized plasmas