The mass shell of the universe

TL;DR

This paper proposes a novel formulation of quantum gravity as a geodesic equation in superspace, introduces a worldline quantization approach, and analyzes the effective action in minisuperspace models, revealing stationary points at zero cosmological constant.

Contribution

It introduces a geodesic-based formulation of gravity and a worldline quantization method, providing new insights into the quantum structure of spacetime.

Findings

Effective action is stationary at zero cosmological constant in certain models.

A hidden mass-shell parameter is identified in the quantization process.

The classical equations reduce to a single geodesic equation in superspace.

Abstract

The classical field equations of general relativity can be expressed as a single geodesic equation, describing the free fall of a point particle in superspace. Based on this formulation, a ``worldline'' quantization of gravity, analogous to the Feynman-Schwinger treatment of particle propagation, is proposed, and a hidden mass-shell parameter is identified. We consider the effective action for the supermetric, which would be induced at one loop. In certain minisuperspace models, we find that this effective action is stationary for vanishing cosmological constant.