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Some aspects of the algebraic quantization programme proposed by Ashtekar arerevisited in this article. It is proved that, for systems with first-classconstraints, the involution introduced on the algebra of quantum operators viareality conditions can never be projected unambiguously to the algebra ofphysical observables, ie, of quantum observables modulo constraints. It isnevertheless shown that, under sufficiently general assumptions, one can stillinduce an involution on the algebra of physical observables from realityconditions, though the involution obtained depends on the choice of particularrepresentatives for the equivalence classes of quantum observables and thisimplies an additional ambiguity in the quantization procedure suggested byAshtekar.Comment: 19 pages, latex, no figure

Involutions on the algebra of physical observables from reality conditions