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GR: Gravitation und Relativitätstheorie

GR 10: Quantengravitation und Quantenkosmologie

GR 10.2: Fachvortrag

Donnerstag, 21. März 2002, 15:00–15:20, HS 20

Attempting to construct a quantum cosmological, dynamically triangulated torus universe in 2+1 dimensions — •Christoph Dehne1 and Renate Loll 21Universität Leipzig, Institut für Theoretische Physik, Augustusplatz 10 - 11, D - 04109 Leipzig (Christoph.Dehne@itp.uni-leipzig.de)
2Universiteit Utrecht, Spinoza Instituut, Minnaertgebouw, Leuvenlaan 4, Postbus 80.195, 3508 TD Utrecht, De Nederlands
(R.Loll@phys.uu.nl)
Using the method of Lorentzian Dynamical Triangulations (LDT) to quantize gravity non-perturbatively, we construct the discretized propagator for one time step in 2+1 dimensions. The topology of the underlying spacetime-manifold is chosen to be T2 × [0,1]. Quantumcosmological symmetries are introduced by requiring that the torus T2 be locally flat at integer values of time t.

If we ask for local flatness also at halfintegers t+1/2, the one-step-propagator for this model can be computed explicitly. We rediscover the kinetic term of the conformal mode, a typical feature of the Euclidian (Hawking) path integral. However, since this model does not seem to have enough entropy to lead to an interesting continuum theory, one can modify this one-step-propagator by dropping the additional condidtion of local flatness at halfintegers. This new model then has enough entropy.

Finally, the relation between the discrete torus parameters of these models and the general expression for the modulus of a flat torus is given.

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