Ponderomotive effects of ultralight dark matter

I exhibit a new class of quadratic effects of ultralight dark matter. Axions, dark photons, and dilatons can exert rapidly oscillating forces, torques, and mass shifts on Standard Model particles. These effects average to zero at first order, but shift particle properties at second order, in analogy to the ponderomotive force in optics. Remarkably, these effects scale with the square of the amplitude of the dark matter field, even when the field’s direct physical effects depend only on its derivatives. I calculate the resulting observables in electron g_e – 2 experiments using classical mechanics, recovering results previously derived using field theory. When considered properly, these particular experiments do not beat astrophysical bounds, but other precision experiments may have interesting sensitivity.