Spacetime geometric structures and the Search for a Quantum Theory of Gravity

TL;DR

This paper discusses the challenge of formulating a background-independent quantum theory of gravity, proposing a gauge-natural formulation of general relativity to explore the structure of spacetime geometries for quantum gravity approaches.

Contribution

It introduces a gauge-natural formulation of general relativity and offers insights into the geometry space structure relevant for non-perturbative quantum gravity and string theory.

Findings

Insights into the structure of the space of geometries

A gauge-natural formulation of general relativity

Implications for non-perturbative quantum gravity

Abstract

One of the biggest challenges to theoretical physics of our time is to find a background-independent quantum theory of gravity. Today one encounters a profusion of different attempts at quantization, but no fully accepted - or acceptable, theory of quantum gravity. Any such approach requires a response to a question that lies at the heart of this problem. ``How shall we resolve the tension between the background dependence of all hitherto-successful quantum theories, both non-relativistic quantum mechanics and special-relativistic quantum field theory, and the background independence of classical general relativity?'' The need for a background-independent quantization procedure forms the starting point of my approach. In this paper I shall present a gauge-natural formulation of general relativity, and provide some insights into the structure of the space of geometries, which plays an important role in the construction of a non-perturbative quantum gravity using a path integral approach, as well as in string theory.