  Similarly to how charged particles experience time-averaged ponderomotive
forces in high-frequency fields, linear waves also experience time-averaged
refraction in modulated media. Here we propose a covariant variational theory
of this "ponderomotive effect on waves" for a general nondissipative linear
medium. Using the Weyl calculus, our formulation accommodates waves with
temporal and spatial period comparable to that of the modulation (provided that
parametric resonances are avoided). Our theory also shows that any wave is, in
fact, a polarizable object that contributes to the linear dielectric tensor of
the ambient medium. The dynamics of quantum particles is subsumed as a special
case. As an illustration, ponderomotive Hamiltonians of quantum particles and
photons are calculated within a number of models. We also explain a fundamental
connection between these results and the commonly known expression for the
electrostatic dielectric tensor of quantum plasmas.
