Global One-Dimensionality conjecture within Quantum General Relativity

TL;DR

This paper introduces a new conjecture in quantum general relativity that simplifies quantum geometrodynamics by relating matter fields to an embedding volume form, leading to a Dirac equation formulation and quantum field theory construction.

Contribution

It proposes a novel conjecture linking matter fields to an embedding volume form, enabling dimensional reduction and a Dirac equation approach in quantum gravity.

Findings

Derivation of a 1D wave function for quantum gravity

Discussion of 3D manifold structures in the model

Association of physical scales with quantum correlations

Abstract

The simple quantum gravity model, based on a new conjecture within the canonically quantized 3+1 general relativity, is presented. The conjecture states that matter fields are functionals of an embedding volume form only, and reduces the quantum geometrodynamics. By dimensional reduction the resulting theory is presented in the form of the Dirac equation, and application of the Fock quantization with the diagonalization procedure yields construction of the appropriate quantum field theory. The 1D wave function is derived, the corresponding 3-dimensional manifolds are discussed, and physical scales are associated with quantum correlations.