Quantum realizations of Hilbert-Palatini second-class constraints

Details Quantum realizations of Hilbert-Palatini second-class constraints Quantum realizations of Hilbert-Palatini second-class constraints

2009-11-03

arxiv.org/abs/0911.0593v2

Class. Quantum Grav.27:145008, 2010

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

Published version

Scientific paper

10.1088/0264-9381/27/14/145008

In a classical theory of gravity, the Barbero-Immirzi parameter ($\eta$) appears as a topological coupling constant through the Lagrangian density containing the Hilbert-Palatini term and the Nieh-Yan invariant. In a quantum framework, the topological interpretation of $\eta$ can be captured through a rescaling of the wavefunctional representing the Hilbert-Palatini theory, as in the case of the QCD vacuum angle. However, such a rescaling cannot be realized for pure gravity within the standard (Dirac) quantization procedure where the second-class constraints of Hilbert-Palatini theory are eliminated beforehand. Here we present a different treatment of the Hilbert-Palatini second-class constraints in order to set up a general rescaling procedure (a) for gravity with or without matter and (b) for any choice of gauge (e.g. time gauge). The analysis is developed using the Gupta-Bleuler and the coherent state quantization methods.

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