On the geometry of quantum constrained systems

Details On the geometry of quantum constrained systems On the geometry of quantum constrained systems

2008-01-08

arxiv.org/abs/0801.1119v2

Class.Quant.Grav.25:135013,2008

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

14 pages, no figures. Discussion expanded. Version published in CQG

Scientific paper

10.1088/0264-9381/25/13/135013

The use of geometric methods has proved useful in the hamiltonian description of classical constrained systems. In this note we provide the first steps toward the description of the geometry of quantum constrained systems. We make use of the geometric formulation of quantum theory in which unitary transformations (including time evolution) can be seen, just as in the classical case, as finite canonical transformations on the quantum state space. We compare from this perspective the classical and quantum formalisms and argue that there is an important difference between them, that suggests that the condition on observables to become physical is through the double commutator with the square of the constraint operator. This provides a bridge between the standard Dirac procedure --through its geometric implementation-- and the Master Constraint program.

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