Hamiltonian analysis of the double null 2+2 decomposition of General Relativity expressed in terms of self-dual bivectors

Abstract

In this paper we obtain a 2+2 double null Hamiltonian description of General Relativity using only the (complex) SO(3) connection and the components of the complex densitised self-dual bivectors. We carry out the general canonical analysis of this system and obtain the first class constraint algebra entirely in terms of the self-dual variables. The first class algebra forms a Lie algebra and all the first class constraints have a simple geometrical interpretation.

arXiv comment12 pages, LaTeX, uses iopart.cls, submitted to Class. Quantum Grav

References in corpus (4)

• Background Independent Quantum Gravity: A Status Report
• Canonical General Relativity on a Null Surface with Coordinate and Gauge Fixing
• Hamiltonian analysis of the double null 2+2 decomposition of Ashtekar variables
• The Vacuum Einstein Equations via Holonomy around Closed Loops on Characteristic Surfaces

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