Quantum gravity as a theory of quantized area bits fitting together

TL;DR

This paper proposes a framework where non-Abelian gauge theories are described in terms of quantized area bits that fit together into closed surfaces, leading to a new understanding of quantum geometry.

Contribution

It introduces a novel relation between area variables and phase space variables, and demonstrates how canonical quantization results in quantized areas with a complete basis of states.

Findings

Derivation of a new equation relating area and phase space variables

Quantization of area bits with a complete orthonormal basis

Interpretation of quantum states as quantized, fitting area bits

Abstract

Non-Abelian Gauss law is interpreted in terms of area bits described in a local frame which fit together into closed surfaces and the Non-Abelian Stokes law in terms of length bits described in a local frame which fit together into closed loops. A new equation relating the area variables and the phase space variables (or equivalently, angular momentum variables of the lattice Yang-Mills theory and phase space variables of the continuum theory) is obtained. Canonical quantization applied to these variables implies area quantization. A complete orthonormal basis of states satisfying the Gauss constraint is obtained.It has the interpretation of quantized area bits with undefined orientations and edges but fitting together into closed surfaces.