From the Einstein-Cartan to the Ashtekar-Barbero canonical constraints, passing through the Nieh-Yan functional

2007/08/31 by Simone Mercuri · 5 citations
Physics and Astronomy · #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #Noncommutative and Quantum Gravity Theories #gr-qc

paper · pdf · doi:10.1103/physrevd.77.024036

published as Phys.Rev.D77:024036,2008 · Minor changes, two references added, accepted for publication in Phys. Rev. D

arxiv created 2008/01/17 · openalex publication_date 2008/01/23 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/30

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.

Citations

• Fermions in Ashtekar-Barbero Connections Formalism for Arbitrary Values of the Immirzi Parameter
• Immirzi parameter in quantum general relativity

Cited by

• Anomalous Majorana neutrino masses from torsionful quantum gravity
• Generalized Ashtekar variables for Palatini f(R) models
• Big bounce and future time singularity resolution in Bianchi I cosmologies: The projective invariant Nieh-Yan case
• Torsional degrees of freedom in AdS4/CFT3
• Parity violation in Poincaré gauge gravity

Related

• Simplified Hamiltonian constraint for a particular value of the Barbero--Immirzi parameter
• Nieh-Yan Invariant and Fermions in Ashtekar-Barbero-Immirzi Formalism
• Fermions in Ashtekar-Barbero Connections Formalism for Arbitrary Values of the Immirzi Parameter
• Lagrangian and Hamiltonian formulations of the Palatini action
• Canonical Electrodynamics in Ashtekar-Barbero variables