From the Einstein-Cartan to the Ashtekar-Barbero canonical constraints, passing through the Nieh-Yan functional
Simone Mercuri
TL;DR
This paper derives the Ashtekar-Barbero constraints in General Relativity with fermions from Einstein-Cartan theory, highlighting the role of the Nieh-Yan functional and the Immirzi parameter in the quantization process.
Contribution
It introduces a novel derivation of Ashtekar-Barbero constraints via rescaling with the Nieh-Yan functional, elucidating the origin of the Immirzi parameter.
Findings
Derivation of Ashtekar-Barbero constraints from Einstein-Cartan theory
Identification of the Immirzi parameter as a quantization ambiguity
Connection between the Nieh-Yan functional and the canonical constraints
Abstract
The Ashtekar-Barbero constraints for General Relativity with fermions are derived from the Einstein-Cartan canonical theory rescaling the state functional of the gravity-spinor coupled system by the exponential of the Nieh-Yan functional. A one parameter quantization ambiguity naturally appears and can be associated with the Immirzi parameter.
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