We have considered the collective effects in 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 semiclassically, but takes into account the interaction among particles in a quantum way. First we apply this method to calculate 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 times͒ of the vector weak-current contribution to neutrino pair emissivity.
͓S0556-2821͑99͒05902-0͔PACS number͑s͒: 97.60. Jd, 13.10.ϩq, 52.25.Tx, 95.30.Cq 1 Note that in the opposite case TӶ 0 , the population of excited Landau levels above the Fermi energy exponentially tends to zero, and the synchrotron radiation becomes not relevant as a mechanism of neutrino pair emission.