Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2004-08-03
Physics
High Energy Physics
High Energy Physics - Theory
Dedicated to John R. Klauder on the occasion of his 70th birthday. To appear in the Proceedings of the Third International Wor
Scientific paper
Coupling any interacting quantum mechanical system to gravity in one (time) dimension requires the cosmological constant to belong to the matter energy spectrum and thus to be quantised, even though the gravity sector is free of any quantum dynamics. Furthermore, physical states are also confined to the subspace of the matter quantum states for which the energy coincides with the value of the cosmological constant. These general facts are illustrated through some simple examples. The physical projector quantisation approach readily leads to the correct representation of such systems, whereas other approaches relying on gauge fixing methods are often plagued by Gribov problems in which case the quantisation rule is not properly recovered. Whether such a quantisation of the cosmological constant as well as the other ensuing consequences in terms of physical states extend to higher dimensional matter-gravity coupled quantum systems is clearly a fascinating open issue.
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