Sergei Alexandrov and Zoltán Kádár 2005 Class. Quantum Grav. 22 3491 doi:10.1088/0264-9381/22/17/010
Sergei Alexandrov and Zoltán Kádár
Show affiliationsWe apply a recently developed canonical formulation of general relativity, which possesses explicit covariance with respect to Lorentz transformations in the tangent space, to describe the case of a timelike foliation of spacetime. Assuming that such a theory based on a timelike foliation makes sense, we derive the spectrum of the area operator of a two-dimensional surface in the framework of the loop quantization. Its different branches are naturally associated with spacelike and timelike surfaces. The results are compared with the predictions of Lorentzian (Barrett–Crane) spin foam models. A restriction of the representations labelling spin networks leads to perfect agreement between the states as well as the area spectra in the two approaches.
Issue 17 (7 September 2005)
Received 7 June 2005
Published 10 August 2005
Sergei Alexandrov and Zoltán Kádár 2005 Class. Quantum Grav. 22 3491
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