  We have considered collective effects in $\nu \bar{\nu}$ synchrotron
radiation from an ultrarelativistic degenerate electron gas in neutron stars
with strong magnetic fields. For this problem we apply a calculation method
which explicitly makes use of the fact that the radiating electron moves
semi-classically, but takes into account the interaction among particles in a
quantum way. First we apply this method to calculate $\nu \bar{\nu}$
synchrotron radiation by an ultrarelativistic electron in vacuum and we compare
this result with that obtained previously by other techniques. When a
degenerate plasma is considered, we show that collective effects lead to an
essential enhancement (about three times) of the vector weak-current
contribution to neutrino pair emissivity.
