  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.
