The century of the incomplete revolution: searching for general relativistic quantum field theory
Carlo Rovelli
TL;DR
The paper argues for a background-independent quantum field theory that unifies quantum mechanics with general relativity via diffeomorphism invariance and relational locality. It juxtaposes canonical loop quantum gravity and covariant spin-foam/topological approaches, showing how discrete quantum geometry (e.g., area spectrum $A(C)=8\pi\hbar G\sum_i\sqrt{j_i(j_i+1)}$) emerges and how BF theory with constraints underpins 4D quantum gravity models like Barrett–Crane. It highlights the convergence of canonical and covariant pictures through spin foams, Turaev–Viro-type state sums, and group-field theory, framing a unified, background-free path integral for gravity. The work suggests that these diffeomorphism-invariant, discretized frameworks may resolve conventional QFT divergences and provide a viable GR limit, pointing toward a new conceptual foundation for fundamental 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.