Journal
FOUNDATIONS OF PHYSICS
Volume 40, Issue 9-10, Pages 1368-1378Publisher
SPRINGER
DOI: 10.1007/s10701-009-9400-z
Keywords
Quantum theory; Time operator; Constraint; Partial observables; Conditional probabilities in quantum physics; Wheeler-De Witt equation
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In the Schrodinger equation, time plays a special role as an external parameter. We show that in an enlarged system where the time variable denotes an additional degree of freedom, solutions of the Schrodinger equation give rise to weights on the enlarged algebra of observables. States in the associated GNS representation correspond to states on the original algebra composed with a completely positive unit preserving map. Application of this map to the functions of the time operator on the large system delivers the positive operator valued maps which were previously proposed by two of us as time observables. As an example we discuss the application of this formalism to the Wheeler-DeWitt theory of a scalar field on a Robertson-Walker spacetime.
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