Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1997-04-23
Atti Accad.Sci.Torino.Sci.Fis.Mat.Natur. 131 (1997) 65-75
Physics
High Energy Physics
High Energy Physics - Theory
10 pages, Plain-TeX. Minor changes in format, nomenclature, and references
Scientific paper
In classical two-dimensional pure dilaton gravity, and in particular in spherically symmetric pure gravity in d dimensions, the generalized Birkhoff theorem states that, for a suitable choice of coordinates, the metric coefficients are only functions of a single coordinate. It is interesting to see how this result is recovered in quantum theory by the explicit construction of the Hilbert space. We examine the CGHS model, enforce the set of auxiliary conditions that select physical states a` la Gupta-Bleuler, and prove that the matrix elements of the metric and of the dilaton field obey the classical requirement. We introduce the mass operator and show that its eigenvalue is the only gauge invariant label of states. Thus the Hilbert space is equivalent to that obtained by quantum mechanical treatment of the static case. This is the quantum form of the Birkhoff theorem for this model.
Alfaro Vittorio de
Cavaglia' Marco
Filippov Alexandre T.
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