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

arXiv comment12 pages

References in corpus (11)

• Metric-Affine Gauge Theory of Gravity: Field Equations, Noether Identities, World Spinors, and Breaking of Dilation Invariance
• The Asymptotic Safety Scenario in Quantum Gravity -- An Introduction
• Spacetime as a Feynman diagram: the connection formulation
• Gravity and the Quantum
• The Universe from Scratch
• Gauge Formalism for General Relativity and Fermionic Matter
• The Hole Argument for Covariant Theories
• A discrete history of the Lorentzian path integral
• Prolegomena to any future Quantum Gravity
• The Hole Argument. Physical Events and the Superspace
• Gauge and General Relativity