GAUGE FIXING, UNITARITY AND PHASE SPACE PATH INTEGRALS

<jats:p> We analyse the extent to which path integral techniques can be used to directly prove the unitarity of gauge theories. After reviewing the limitations of the most widely used approaches, we concentrate upon the method which is commonly regarded as solving the problem, i.e. that of Fradkin and Vilkovisky. We show through explicit counterexamples that their main theorem is incorrect. A proof is presented for a restricted version of their theorem. From this restricted theorem we are able to rederive Faddeev’s unitary phase space results for a wide class of canonical gauges (which includes the Coulomb gauge) and for the Feynman gauge. However, we show that there are serious problems with the extensions of this argument to the Landau gauge and hence the full Lorentz class. We conclude that there does not yet exist any satisfactory path integral discussion of the covariant gauges. </jats:p>