To write down a path integral for the Ashtekar gravity one must solve three
fundamental problems. First, one must understand the rules of complex cont
our functional integration with holomorphic action. Second, one should find
which gauges are compatible with reality conditions. Third, one should eva
luate the Faddeev-Popov determinant produced by these conditions. In the pr
esent paper we derive the ERST path integral for Hilbert-Palatini gravity.
We show that for a certain class of gauge conditions this path integral can
be rewritten in terms of the Ashtekar variables. Reality conditions define
contours of integration, For our class of gauges all ghost terms coincide
with what one could write naively, just ignoring any Jacobian factors arisi
ng from the reality conditions, [S0556-2821(98)06824-6].