Real and complex connections for canonical gravity
- 1 October 1997
- journal article
- letter
- Published by IOP Publishing in Classical and Quantum Gravity
- Vol. 14 (10) , L177-L181
- https://doi.org/10.1088/0264-9381/14/10/002
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.Keywords
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This publication has 15 references indexed in Scilit:
- Quantum theory of geometry: I. Area operatorsClassical and Quantum Gravity, 1997
- Volume and quantizationsClassical and Quantum Gravity, 1997
- Stochastic path integrals and open quantum systemsPhysical Review A, 1996
- Quantizing Regge calculusClassical and Quantum Gravity, 1996
- Reality conditions inducing transforms for quantum gauge field theory and quantum gravityClassical and Quantum Gravity, 1996
- Production or annihilation of positrons with bound electronsPhysical Review A, 1996
- Real Ashtekar variables for Lorentzian signature space-timesPhysical Review D, 1995
- Weaving a classical metric with quantum threadsPhysical Review Letters, 1992
- New Hamiltonian formulation of general relativityPhysical Review D, 1987
- New Variables for Classical and Quantum GravityPhysical Review Letters, 1986