Discrete Hamiltonian for General Relativity

TL;DR

This paper derives a holographic Hamiltonian for general relativity using loop gravity variables, enabling straightforward quantization by fixing gauge within a cellular decomposition.

Contribution

It introduces a novel gauge-fixing approach in the Ashtekar formulation leading to a boundary-based holographic description of gravity.

Findings

Holographic bulk dynamics are captured by boundary degrees of freedom.

The derived Hamiltonian is compatible with existing quantization methods.

The approach simplifies the path to quantum gravity models.

Abstract

Beginning from the Ashtekar formulation of canonical general relativity, we derive a physical Hamiltonian written in terms of (classical) loop gravity variables. This is done by gauge-fixing the gravitational fields within a complex of three-dimensional cells such that curvature and torsion vanish within each cell. The resulting theory is holographic, with the bulk dynamics being captured completely by degrees of freedom living on cell boundaries. Quantization is readily obtainable by existing methods.