Gauge and spacetime connections in the Plebanski formulation of complex general relativity
General Relativity and Quantum Cosmology
2013-01-28 v2 High Energy Physics - Theory
Differential Geometry
Abstract
The Plebanski formulation of complex general relativity is given in terms of variables valued in the complexification of the Lie algebra. Therefore, it is genuinely a gauge theory that is also diffeomorphism-invariant. For this reason, the way that the Levi-Civita connection emerges from this formulation is not direct because both the internal (gauge) and the spacetime connections are geometrical structures a priori not related, there is not a natural link between them. Any possible relationship must be put in by hand or must come from extra hypotheses. In this paper, we analyze the correct relationship between these connections and show how they are related.
Keywords
Cite
@article{arxiv.1204.4225,
title = {Gauge and spacetime connections in the Plebanski formulation of complex general relativity},
author = {Diego Gonzalez and Merced Montesinos and Mercedes Velazquez},
journal= {arXiv preprint arXiv:1204.4225},
year = {2013}
}
Comments
LaTeX File