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#### On the role of the Barbero-Immirzi parameter in discrete quantum gravity

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##### Fulltext (public)

1209.4892

(Preprint), 4KB

CQG_30_9_095015.pdf

(Any fulltext), 2MB

##### Supplementary Material (public)

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##### Citation

Dittrich, B., & Ryan, J. P. (2013). On the role of the Barbero-Immirzi parameter
in discrete quantum gravity.* Classical and quantum gravity,* *30*(9):
095015.

Cite as: http://hdl.handle.net/11858/00-001M-0000-000E-EB27-2

##### Abstract

The 1-parameter family of transformations identified by Barbero and Immirzi
plays a significant role in non-perturbative approaches to quantum gravity,
among them Loop Quantum Gravity and Spin Foams. It facilitates the loop
quantization programme and subsequently the Barbero-Immirzi parameter (gamma)
arises in both the spectra of geometrical operators and in the dynamics
provided by Spin Foams. However, the debate continues as to whether quantum
physics should be Barbero-Immirzi parameter dependent. Starting from a discrete
SO(4)-BF theory phase space, we find two possible reductions with respect to a
discrete form of the simplicity constraints. The first reduces to a phase space
with gamma-dependent symplectic structure and more generally in agreement with
the phase space underlying Loop Quantum Gravity restricted to a single graph -
a.k.a. Twisted Geometries. The second, fuller reduction leads to a
gamma-independent symplectic structure on the phase space of
piecewise-flat-linear geometries - a.k.a. Regge geometries. Thus, the
gamma-dependence of physical predictions is related to the choice of phase
space underlying the quantization.