Metric Versus Ashtekar Variables in Two Killing Field Reduced Gravity

Details Metric Versus Ashtekar Variables in Two Killing Field Reduced Gravity Metric Versus Ashtekar Variables in Two Killing Field Reduced Gravity

1997-10-30

arxiv.org/abs/gr-qc/9710133v1

Class.Quant.Grav. 15 (1998) 1367-1374

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

9 pages, LaTeX2e

Scientific paper

10.1088/0264-9381/15/5/018

The relation between the SL(2,R)/SO(2)- and the SL(2,C)-chiral model that naturally arise within the metric respectively the Ashtekar formulation of two Killing field reduced Einstein gravity is revealed. Both chiral models turn out to be completely equivalent even though the transition from the coset- to the SL(2,C)-model is accompanied by a disappearance of the non-ultralocal terms in the Poisson brackets.

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