Year: 1994
Type: article
Abstract: Starting from the Ashtekar Hamiltonian variables for general relativity, the self-dual Einstein equations (SDE) may be rewritten as evolution equations for three divergence-free vector fields given on a three-dimensional surface with a fixed volume element. From this general form of the SDE, it is shown how they may be interpreted as the field equations for a two-dimensional field theory. It is further shown that these equations imply an infinite number of non-local conserved currents. A specific way of writing the vector fields allows an identification of the full SDE with those of the two-dimensional chiral model, with the gauge group being the group of area-preserving diffeomorphisms of a two-dimensional surface. This gives a natural Hamiltonian formulation of the SDE in terms of that of the chiral model.
Source: Classical and Quantum Gravity
Author: Viqar Husain
Institution: University of Alberta
Language: English
Subfield: Astronomy and Astrophysics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: bronze
OpenAlex ID: W2144201655