Covariant Loop Quantum Gravity

This textbook presents a formal introduction to the covariant version of loop quantum gravity, often referred to as the spinfoam formalism. Rovelli and Vidotto construct a framework that attempts to reconcile general relativity with quantum mechanics by treating spacetime as a collection of discrete, quantized units rather than a smooth background. The authors detail the transition from classical structures to quantum tetrahedra, explaining how spin networks represent spatial geometry and how spinfoams describe the evolution of these geometries over time. They derive the specific mathematical language of the theory, including the EPRL-FK amplitude and the transition from the canonical formulation to the sum-over-histories approach.

Graduate students and theoretical physicists read this book to master the technical tools of background-independent quantum gravity. Because it bypasses the traditional perturbative methods of string theory, it serves those interested in the fundamental structure of space and time at the Planck scale. A reader finishes the text with the ability to calculate transition amplitudes and use the covariant framework to address cosmological problems, such as the behavior of black holes or the physics of the early universe.