An introduction to quantum gravity

TL;DR

This paper introduces quantum gravity, exploring its theoretical foundations, competing theories like string theory and loop quantum gravity, and discussing recent developments, mathematical insights, and experimental challenges in unifying quantum mechanics and general relativity.

Contribution

It provides a comprehensive review of the classical and quantum foundations of quantum gravity, highlighting recent theoretical progress and the status of observational tests.

Findings

Analysis of classical and quantum foundations of quantum gravity

Discussion of string theory and loop quantum gravity

Overview of experimental challenges in quantum gravity

Abstract

Quantum gravity was born as that branch of modern theoretical physics that tries to unify its guiding principles, i.e., quantum mechanics and general relativity. Nowadays it is providing new insight into the unification of all fundamental interactions, while giving rise to new developments in mathematics. The various competing theories, e.g. string theory and loop quantum gravity, have still to be checked against observations. We review the classical and quantum foundations necessary to study field-theory approaches to quantum gravity, the passage from old to new unification in quantum field theory, canonical quantum gravity, the use of functional integrals, the properties of gravitational instantons, the use of spectral zeta-functions in the quantum theory of the universe, Hawking radiation, some theoretical achievements and some key experimental issues.