Real and complex connections for canonical gravity

1996/12/12 by Giorgio Immirzi · 13 citations
Physics and Astronomy · #Black Holes and Theoretical Physics #Canonical quantization #Canonical quantum gravity #Connection (principal bundle) #Cosmology and Gravitation Theories #Gauge (firearms) #Gauge theory #Hamiltonian (control theory) #Noncommutative and Quantum Gravity Theories #Poisson bracket #Quantum #Quantum gravity #gr-qc

paper · pdf · doi:10.1088/0264-9381/14/10/002

published as Class.Quant.Grav.14:L177-L181,1997 · 8 pages, RevTeX, no figures

arxiv created 1996/12/12 · openalex publication_date 1997/10/01 · arxiv updated 2010/04/06 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/06

Abstract

Both real and complex connections have been used for canonical gravity: the complex connection has SL(2,C) as the gauge group, while the real connection has SU(2) as the gauge group. We show that there is an arbitrary parameter which enters in the definition of the real connection, in the Poisson brackets, and therefore in the scale of the discrete spectra one finds for areas and volumes in the corresponding quantum theory. A value for could be singled out in the quantum theory by the Hamiltonian constraint or by the rotation to the complex Ashtekar connection.

Citations

• Knot Theory and Quantum Gravity
• Anomaly-free formulation of non-perturbative, four-dimensional Lorentzian quantum gravity
• Thermodynamics of Spacetime: The Einstein Equation of State
• New Variables for Classical and Quantum Gravity
• New Hamiltonian formulation of general relativity
• Real Ashtekar variables for Lorentzian signature space-times
• Black Hole Entropy from Loop Quantum Gravity

Cited by

• Immirzi ambiguity in the kinematics of quantum general relativity
• Loop Quantum Cosmology
• Einstein-Cartan wormhole solutions
• Proof of Bekenstein–Mukhanov ansatz in loop quantum gravity
• Spin foam models for quantum gravity
• Revisiting the solution of the second-class constraints of the Holst action
• Deformed general relativity and effective actions from loop quantum gravity
• The Reduced Phase Space of Palatini–Cartan–Holst Theory
• The length operator in Loop Quantum Gravity
• Commuting simplicity and closure constraints for 4D spin-foam models
• Lemaitre-Tolman-Bondi collapse from the perspective of loop quantum gravity
• Torsion at Different Scales: From Materials to the Universe
• Area spectrum and black hole thermodynamics