  We derive semiclassical neutrino-electron transport equations in the
collisionless (Vlasov) limit from the coupled Dirac equations, incorporating
the charged and neutral weak current-current as well as electromagnetic
interactions. A corresponding linear response theory is derived. In particular,
we calculate the response functions for a variety of beam-plasma geometries,
which are of interest in a supernova scenario. We apply this to the study of
plasmons and to a new class of collective {\it pharon} resonance modes, which
are characterized by $\omega < q$. We find that the growth rates of the
unstable modes correspond to a strongly temperature ($\propto T_\nu^2T_e^3$)
and linearly momentum dependent e-folding length of about $10^{10}$ km under
typical conditions for Type II supernovae. This appears to rule out such
long-wavelength collective modes as an efficient means of depositing neutrino
energy into the plasma sphere.
