Involutions on the Algebra of Physical Observables From Reality Conditions

Details Involutions on the Algebra of Physical Observables From Reality Conditions Involutions on the Algebra of Physical Observables From Reality Conditions

1995-06-20

arxiv.org/abs/gr-qc/9506038v1

J.Math.Phys. 37 (1996) 196-205

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

19 pages, latex, no figures

Scientific paper

10.1063/1.531383

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.

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