  Some aspects of the algebraic quantization programme proposed by Ashtekar are
revisited in this article. It is proved that, for systems with first-class
constraints, the involution introduced on the algebra of quantum operators via
reality conditions can never be projected unambiguously to the algebra of
physical observables, ie, of quantum observables modulo constraints. It is
nevertheless shown that, under sufficiently general assumptions, one can still
induce an involution on the algebra of physical observables from reality
conditions, though the involution obtained depends on the choice of particular
representatives for the equivalence classes of quantum observables and this
implies an additional ambiguity in the quantization procedure suggested by
Ashtekar.
