Wick transform and physical states in 2+1 loop quantum gravity

Details Wick transform and physical states in 2+1 loop quantum gravity Wick transform and physical states in 2+1 loop quantum gravity

Apr 2002

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2002aps..apri12002w&link_type=abstract

American Physical Society, April Meeting, Jointly Sponsored with the High Energy Astrophysics Division (HEAD) of the American As

Astronomy and Astrophysics

Astrophysics

Scientific paper

We investigate different formulations of 2+1 dimensional classical general relativity in connection variables. In particular, we find that Lorentzian theory can be written in such a way that the gauge group is compact. This allows us to define maps which we call Wick rotation and Wick transform. They relate the standard Euclidean and Lorentzian formulations of 2+1 gravity. At the quantum level, operator corresponding to the Wick transform, maps physical states of Euclidean theory to physical states of Lorentzian theory. We provide detailed construction of this operator on the space spanned by functions of flat connections. States with support only on flat connections naturally provide semi-classical states in the theory. We explain a construction of elementary quantum states in physical Hilbert space which superposed provide the semi-classical solutions.

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