2000/05/31 by Joseph Samuel · 80 citations
Physics and Astronomy · #Canonical quantum gravity #Connection (principal bundle) #Diffeomorphism #Gauge fixing #Gauge theory #General relativity #Hamiltonian (control theory) #Hamiltonian lattice gauge theory #Noncommutative and Quantum Gravity Theories #Quantum Mechanics and Applications #Relativity and Gravitational Theory #Wheeler–DeWitt equation #gr-qc
paper · pdf · doi:10.1088/0264-9381/17/20/101
published in Classical and Quantum Gravity 17(20), L141-L148 (IOP Publishing) · 12 pages, no figures, revised in the light of referee's comments, accepted for publication in Classical and Quantum Gravity
arxiv created 2000/09/20 · openalex publication_date 2000/09/26 · arxiv updated 2010/04/06 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
This letter is a critique of Barbero's constrained Hamiltonian formulation of general relativity, on which current work in loop quantum gravity is based. While we do not dispute the correctness of Barbero's formulation of general relativity, we offer some criticisms of an aesthetic nature. We point out that unlike Ashtekar's complex SU (2) connection, Barbero's real SO (3) connection does not admit an interpretation as a space-time gauge field. We show that if one tries to interpret Barbero's real SO (3) connection as a space-time gauge field, the theory is not diffeomorphism invariant. We conclude that Barbero's formulation is not a gauge theory of gravity in the sense that Ashtekar's Hamiltonian formulation is. The advantages of Barbero's real connection formulation have been bought at the price of giving up the description of gravity as a gauge field.