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Quantum realizations of Hilbert-Palatini second-class constraints · Around

2009

Quantum realizations of Hilbert-Palatini second-class constraints

Sengupta, Sandipan

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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.

Built on

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