An introduction to quantum gravity

TL;DR

This paper provides a pedagogical overview of quantum gravity, including formal structure, quantization methods, and selected advanced topics like braneworld models and spectral asymptotics, aimed at students and educators.

Contribution

It reprints DeWitt's foundational lectures on quantum gravity's formal structure and discusses recent topics like braneworlds and spectral analysis within a covariant framework.

Findings

Functional integral quantization of gravity explained

Spectral asymptotics may help in singularity avoidance

Braneworld models analyzed with covariant formalism

Abstract

After an overview of the physical motivations for studying quantum gravity, we reprint THE FORMAL STRUCTURE OF QUANTUM GRAVITY, i.e. the 1978 Cargese Lectures by Professor B.S. DeWitt, with kind permission of Springer. The reader is therefore introduced, in a pedagogical way, to the functional integral quantization of gravitation and Yang-Mills theory. It is hoped that such a paper will remain useful for all lecturers or Ph.D. students who face the task of introducing (resp. learning) some basic concepts in quantum gravity in a relatively short time. In the second part, we outline selected topics such as the braneworld picture with the same covariant formalism of the first part, and spectral asymptotics of Euclidean quantum gravity with diffeomorphism-invariant boundary conditions. The latter might have implications for singularity avoidance in quantum cosmology.