Fundamental Physics with Charged Particle Measurements at the Cherenkov Telescope Array

Cosmic electrons, positrons, protons, and antiprotons carry essential information about both astrophysical processes and fundamental physics. Charged particles provide signatures of dark matter annihilation or decay, \emph{in situ} in the universe, that are complementary to the other messengers of indirect dark matter detection, gamma rays and neutrinos. We discuss the science potential for measurements of charged particles by the Cherenkov Telescope Array (CTA), an instrument under development primarily for the study of cosmic gamma rays with energies $30\ \textrm{GeV} - 200\ \textrm{TeV}$.