On the quantization of the Null-Surface formulation of GR

TL;DR

This paper introduces quantum operators for spacetime geometry in quantum general relativity, combining the Null-Surface Formulation with asymptotic quantization, revealing a 'fuzzy' quantum light cone and point structure.

Contribution

It develops a novel framework of quantum spacetime operators based on the Null-Surface Formulation, providing new insights into quantum geometry.

Findings

Quantum operators describe 'fuzzy' light cone structure.

Spacetime-point operators characterize physical points.

Derived commutation algebra around flat space.

Abstract

We define and discuss various quantum operators that describe the geometry of spacetime in quantum general relativity. These are obtained by combining the Null-Surface Formulation of general relativity, recently developed, with asymptotic quantization. One of the operators defined describes a ``fuzzy'' quantum light cone structure. Others, denoted ``spacetime-point operators'', characterize geometrically-defined physical points. We discuss the interpretation of these operators. This seems to suggest a picture of quantum spacetime as made of ``fuzzy'' physical points. We derive the commutation algebra of the quantum spacetime point operators in the linearization around flat space.