Immirzi ambiguity in the kinematics of quantum general relativity



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Garay Elizondo, Luis Javier and Mena Marugán, Guillermo A. (2002) Immirzi ambiguity in the kinematics of quantum general relativity. Physical review D, 66 (2). ISSN 0556-2821

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The Immirzi ambiguity arises in loop quantum gravity when geometric operators are represented in terms of different connections that are related by means of an extended Wick transform. We analyze the action of this transform in gravity coupled with matter fields and discuss its analogy with the Wick rotation on which the Thiemann transform between Euclidean and Lorentzian gravity is based. In addition, we prove that the effect of this extended Wick transform is equivalent to a constant scale transformation as far as the symplectic structure and kinematical constraints are concerned. This equivalence is broken in the dynamical evolution. Our results are applied to the discussion of the black hole entropy in the limit of large horizon areas. We first argue that, since the entropy calculation is performed for horizons of fixed constant area, one might in principle choose an Immirzi parameter that depends on this quantity. This would spoil the linearity with the area in the entropy formula. We then show that the Immirzi parameter appears as a constant scaling in all the steps where dynamical information plays a relevant role in the entropy calculation. This fact, together with the kinematical equivalence of the Immirzi ambiguity with a change of scale, is used to preclude the potential nonlinearity of the entropy on physical grounds.

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© 2002 The American Physical Society.
G.A.M.M. is very thankful to J.F. Barbero G. for enlightening discussions. This work was supported by funds provided by the Spanish Ministry of Science and Technology under the Research Project No. BFM2001-0213.

Uncontrolled Keywords:Hamiltonian-formulation; Gravity; Parameter; Variables; Matter; Real
Subjects:Sciences > Physics > Physics-Mathematical models
Sciences > Physics > Mathematical physics
ID Code:29883
Deposited On:30 Apr 2015 08:28
Last Modified:10 Dec 2018 15:10

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