Lagrangian geometrical optics of nonadiabatic vector waves and spin particles

摘要: Abstract Linear vector waves, both quantum and classical, experience polarization-driven bending of ray trajectories polarization dynamics that can be interpreted as the precession “wave spin”. Both phenomena are governed by an effective gauge Hamiltonian vanishing in leading-order geometrical optics. This recognized a generalization Stern–Gerlach is commonly known for spin-1/2 particles. The corresponding reduced Lagrangians continuous nondissipative waves their geometrical-optics rays derived from fundamental wave Lagrangian. resulting Euler–Lagrange equations describe simultaneous interactions N resonant modes, where arbitrary, lead to spin, which happens ( 2 − 1 ) -dimensional spin vector. As special case, classical Dirac particle = deduced formally, without introducing additional postulates or interpretations, Lagrangian with Pauli term. model reproduces Bargmann–Michel–Telegdi added force.