2000/09/07 by Alejandro Perez, Alejandro Pérez, Carlo Rovelli · 108 citations
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Black Holes and Theoretical Physics #Classical mechanics #Combinatorics #Euclidean geometry #General relativity #Generalization #Geometry #Group field theory #Loop quantum gravity #Mathematical analysis #Mathematical physics #Mathematics #Noncommutative and Quantum Gravity Theories #Physics #Quantum #Quantum gravity #Quantum mechanics #Simple (philosophy) #Spin (aerodynamics) #Spin foam #Theoretical physics #Theory of relativity #Vertex (graph theory) #gr-qc
paper · pdf · doi:10.1103/physrevd.63.041501
published in Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields 63(4) (American Physical Society) · 8 pages, 1 figure
arxiv created 2000/09/07 · openalex publication_date 2001/01/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We present a spin foam formulation of Lorentzian quantum general relativity. The theory is based on a simple generalization of a Euclidean model defined in terms of a field theory over a group. Its vertex amplitude turns out to be the one recently introduced by Barrett and Crane. As in the case of its Euclidean relatives, the model fully implements the desired sum over 2-complexes which encodes the local degrees of freedom of the theory.