Quantum realizations of Hilbert-Palatini second-class constraints

Abstract

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.

Published version

References in corpus (3)

• Testing the Master Constraint Programme for Loop Quantum Gravity II. Finite Dimensional Systems
• Topological Interpretation of Barbero-Immirzi Parameter
• From the Einstein-Cartan to the Ashtekar-Barbero canonical constraints, passing through the Nieh-Yan functional

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• SU(2) gauge theory of gravity with topological invariants
• Modifications in the Spectrum of Primordial Gravitational Waves Induced by Instantonic Fluctuations
• Torsional instanton effects in quantum gravity
• Dark Energy From The Gravity Vacuum