  We have recently shown that the electromagnetic field in a medium is made of
mass-polariton (MP) quasiparticles, which are quantized coupled states of the
field and an atomic mass density wave (MDW) [Phys. Rev. A 95, 063850 (2017)].
In this work, we generalize the MP theory of light for dispersive media
assuming that absorption and scattering losses are very small. Following our
previous work, we present two different approaches to the theory of light: (1)
the MP quasiparticle theory, which is derived by only using the fundamental
conservation laws and the Lorentz transformation; (2) the classical optoelastic
continuum dynamics (OCD), which is a generalization of the electrodynamics of
continuous media to include the dynamics of the medium under the influence of
optical forces. For the coupled MP state of a single photon and the medium, we
obtain the total MP momentum of the Minkowski form while the field's share of
the momentum is equal to the Abraham momentum. We also show that the
correspondence between the MP and OCD models and the conservation of momentum
at interfaces gives an unambiguous formula for the optical force. The dynamics
of the light pulse and the related MDW lead to nonequilibrium of the medium and
to relaxation of the atomic density by sound waves in the same way as for
nondispersive media. We also carry out simulations for optimal measurements of
atomic displacements related to the MDW in silicon. In the simulations, we
consider different waveguide cross-sections and optical pulse widths and
account for the breakdown threshold irradiance of materials. We also compare
the MP theory to previous theories of the momentum of light in a dispersive
medium. We show that our generalized MP theory resolves all the problems
related to the Abraham-Minkowski dilemma in a dispersive medium.
