  The surface of a Weyl semimetal (WSM) displays Fermi arcs, i.e. disjoint
segments of a two-dimensional Fermi contour. We present a quantum-mechanical
non-local theory of chiral Fermi arc plasmons in WSMs with broken time-reversal
symmetry. These are collective excitations constructed from topological Fermi
arc and bulk electron states and arising from electron-electron interactions,
which are treated in the realm of the random phase approximation. Our theory
includes quantum effects associated with the penetration of the Fermi arc
surface states into the bulk and dissipation, which is intrinsically non-local
in nature and arises from decay processes mainly involving bulk electron-hole
pair excitations.
