New Loop Representations for 2+1 Gravity

Details New Loop Representations for 2+1 Gravity New Loop Representations for 2+1 Gravity

1994-05-12

arxiv.org/abs/gr-qc/9405031v1

Class.Quant.Grav.11:2417-2434,1994

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

28pp, 1 figure (postscript, compressed and uuencoded), TeX, Pennsylvania State University, CGPG-94/5-1

Scientific paper

10.1088/0264-9381/11/10/004

Since the gauge group underlying 2+1-dimensional general relativity is non-compact, certain difficulties arise in the passage from the connection to the loop representations. It is shown that these problems can be handled by appropriately choosing the measure that features in the definition of the loop transform. Thus, ``old-fashioned'' loop representations - based on ordinary loops - do exist. In the case when the spatial topology is that of a two-torus, these can be constructed explicitly; {\it all} quantum states can be represented as functions of (homotopy classes of) loops and the scalar product and the action of the basic observables can be given directly in terms of loops.

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