Ulm 2004 – wissenschaftliches Programm

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GR: Gravitation und Relativitätstheorie

GR 1: Quantengravitation und Quantenkosmologie

GR 1.4: Fachvortrag

Montag, 15. März 2004, 15:20–15:40, H20

Group averaging in the (p,q) oscillator representation of SL(2,R) — •Jorma Louko and Alberto Molgado — School of Mathematical Sciences, University of Nottingham, Nottingham NG7 2RD, United Kingdom

We investigate refined algebraic quantisation with group averaging in a finite-dimensional constrained Hamiltonian system that provides a simplified model of general relativity. The classical theory has gauge group SL(2,R) and a distinguished O(p,q) observable algebra. The gauge group of the quantum theory is the double cover of SL(2,R), and its representation on the auxiliary Hilbert space is isomorphic to the (p,q) oscillator representation. When p≥2, q≥2 and p+q ≡ 0 (mod 2 ), we obtain a physical Hilbert space with a nontrivial representation of the O(p,q) quantum observable algebra. For p=q=1, the system provides the first example known to us where group averaging converges to an indefinite sesquilinear form.