Physics – Mathematical Physics
Scientific paper
2009-09-10
Physics
Mathematical Physics
13 pages, typos correction plus added conclusion section, accepted on Foundations of Physics, proceedings of the "Festschrift
Scientific paper
In the Schroedinger 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 Schroedinger 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.
Brunetti Romeo
Fredenhagen Klaus
Hoge Marc
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