Hamiltonian analysis of the double null 2+2 decomposition of Ashtekar variables

Abstract

We derive a canonical analysis of a double null 2+2 Hamiltonian description of General Relativity in terms of complex self-dual 2-forms and the associated SO(3) connection variables. The algebra of first class constraints is obtained and forms a Lie algebra that consists of two constraints that generate diffeomorphisms in the two surface, a constraint that generates diffeomorphisms along the null generators and a constraint that generates self-dual spin and boost transformations.

arXiv comment17 pages, LaTeX uses iopart.cls, to appear in Class. Quantum Grav

References in corpus (5)

• Background Independent Quantum Gravity: A Status Report
• Quantum Spin Dynamics (QSD)
• Canonical General Relativity on a Null Surface with Coordinate and Gauge Fixing
• Hamiltonian analysis of the double null 2+2 decomposition of General Relativity expressed in terms of self-dual bivectors
• Ashtekar Variables in Classical General Realtivity

Cited by in corpus (8)

• A covariant action principle for dissipative fluid dynamics: From formalism to fundamental physics
• First order gravity on the light front
• Sachs' free data in real connection variables
• Hamiltonian analysis of the double null 2+2 decomposition of General Relativity expressed in terms of self-dual bivectors
• Gravitational Constraints on a Lightlike boundary
• Prolegomena to any future Quantum Gravity
• Hamiltonian Analysis of 3-dimensional Spacetime in Bondi-like Coordinates
• Hamiltonian Analysis of 4-dimensional Spacetime in Bondi-like Coordinates