BATALIN-FRADKIN QUANTIZATION OF THE UNITARY GAUGE ABELIAN HIGGS-MODEL

In the unitary gauge the abelian Higgs model is a second-class system with non-polynomial field dependent Dirac brackets. We quantize this theory following Batalin and Fradkin, by first converting it into a first-class system in an extended phase space, and then constructing the unitarizing Hamiltonian and the BRST charge. In particular we show how the partition function of the first-class and second-class (unitary gauge) formulations is recovered for different choices of gauge conditions in the extended phase space. In Faddeev-Popov-like gauges, the auxiliary Batalin-Fradkin scalar field is identified with the Goldstone boson of the Higgs model.