Zakopane lectures on loop gravity

TL;DR

Zakopane lectures present a self-contained, covariant formulation of loop quantum gravity (LQG) built on spin-network kinematics and spinfoam dynamics. The text explains how SU(2) representation theory, graph-based Hilbert spaces, and SL(2,C) covariant amplitudes combine to yield a finite, background-independent quantum gravity framework whose semiclassical limit recovers Regge calculus and general relativity. It then develops coherent-state techniques, holomorphic representations, Euclidean/Lorentzian variants, and systematic two-complex/graph expansions, with concrete cosmological and n-point function results illustrating viability. The notes also cover derivations, covariant lattice quantization, and polyhedral quantum geometry, and they outline open problems and directions toward a complete theory. Overall, the work argues for LQG as a coherent, predictive approach to quantum gravity that unifies GR with quantum theory in a background-independent setting and motivates further phenomenological and mathematical development.

Abstract

These are introductory lectures on loop quantum gravity. The theory is presented in self-contained form, without emphasis on its derivation from classical general relativity. Dynamics is given in the covariant form. Some applications are described.

Figures (10)

• Figure 1: A spin network and the "quanta of space" it describes.
• Figure 2: A simple two-complex with one internal vertex.
• Figure 3: Picturing of an graph with $N=8$ and $L=10$.
• Figure 4: Normals (here arrows) to the faces, and proportional to the area of the face, satisfy \ref{['closure']} and uniquely determine the polyhedron (here a tetrahedron).
• Figure 5: "Granular" space. A node $n$ determines a "grain" or "chunk" of space.