The century of the incomplete revolution: searching for general relativistic quantum field theory

TL;DR

This paper reviews the quest for a unified framework of quantum field theory compatible with general relativity, highlighting diverse approaches like topological theories, string theory, spin foam models, and loop quantum gravity, and their interrelations.

Contribution

It synthesizes various approaches to formulating a generally relativistic quantum field theory, emphasizing their connections and the overarching conceptual framework.

Findings

Examples of covariant relativistic quantum theories include topological QFTs and spin foam models.

Loop quantum gravity offers a canonical approach to relativistic quantum field theory.

Diverse approaches are interconnected, suggesting a unified picture of relativistic quantum physics.

Abstract

In fundamental physics, this has been the century of quantum mechanics and general relativity. It has also been the century of the long search for a conceptual framework capable of embracing the astonishing features of the world that have been revealed by these two ``first pieces of a conceptual revolution''. I discuss the general requirements on the mathematics and some specific developments towards the construction of such a framework. Examples of covariant constructions of (simple) generally relativistic quantum field theories have been obtained as topological quantum field theories, in nonperturbative zero-dimensional string theory and its higher dimensional generalizations, and as spin foam models. A canonical construction of a general relativistic quantum field theory is provided by loop quantum gravity. Remarkably, all these diverse approaches have turn out to be related, suggesting an intriguing general picture of general relativistic quantum physics.