Superspace Dynamics and Perturbations Around "Emptiness"

TL;DR

This paper explores superspace parametrized by gauge potentials within the Ashtekar variables framework, identifying an internal clock, deriving gauge-fixing conditions, and presenting a perturbation scheme around an unconventional background, maintaining simplicity of the formulation.

Contribution

It introduces a novel superspace approach using gauge potentials, identifies an internal clock, and develops a perturbation scheme around a unique background in Ashtekar's formulation.

Findings

Identification of an internal clock in superspace

Derivation of gauge-fixing conditions separating physical and gauge modes

Development of a perturbation scheme around an unconventional background

Abstract

Superspace parametrized by gauge potentials instead of metric three-geometries is discussed in the context of the Ashtekar variables. Among other things, an "internal clock" for the full theory can be identified. Gauge-fixing conditions which lead to the natural geometrical separation of physical from gauge modes are derived with the use of the metric in connection-superspace. A perturbation scheme about an unconventional background which is inaccessible to conventional variables is presented. The resultant expansion retains much of the simplicity of Ashtekar's formulation of General Relativity.