RT Journal Article
T1 Immirzi ambiguity in the kinematics of quantum general relativity
A1 Garay Elizondo, Luis Javier
A1 Mena Marugán, Guillermo A.
AB 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.
PB Amer Physical Soc
SN 0556-2821
YR 2002
FD 2002-07-15
LK https://hdl.handle.net/20.500.14352/59513
UL https://hdl.handle.net/20.500.14352/59513
LA eng
NO © 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.
NO Spanish Ministry of Science and Technology
DS Docta Complutense
RD 29 abr 2025