  Collective charge excitations in solids have been the subject of intense
research ever since the pioneering works of Bohm and Pines in the 1950s. Most
of these studies focused on long-wavelength plasmons that involve charge
excitations with a small crystal-momentum transfer, $q \ll G$, where $G$ is the
wavenumber of a reciprocal lattice vector. Less emphasis was given to
collective charge excitations that lead to shortwave plasmons in multivalley
electronic systems (i.e., when $q \sim G$). We present a theory of intervalley
plasmons, taking into account local-field effects in the dynamical dielectric
function. Focusing on monolayer transition-metal dichalcogenides where each of
the valleys is further spin-split, we derive the energy dispersion of these
plasmons and their interaction with external charges. Emphasis in this work is
given to sum rules from which we derive the interaction between intervalley
plasmons and a test charge, as well as a compact single-plasmon pole expression
for the dynamical Coulomb potential.
