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

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.

arXiv commentMinor changes, two references added, accepted for publication in Phys. Rev. D

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• Chern-Simons Modified Gravity as a Torsion Theory and its Interaction with Fermions
• Big Bounce cosmology for Palatini $R^2$ gravity with a Nieh-Yan term
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• Seeking the Loop Quantum Gravity Barbero-Immirzi Parameter and Field in 4D, $\mathcal{N}$ = 1 Supergravity
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• Holst Actions for Supergravity Theories
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• Torsion in string-inspired cosmologies and the universe dark sector
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• Generalized Ashtekar variables for Palatini f(R) models
• Torsional Topological Invariants
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• Hamiltonian analysis of SO(4,1) constrained BF theory
• Implications of the Holst term in a $f(R)$ theory with torsion
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• Barbero-Immirzi parameter, manifold invariants and Euclidean path integrals
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• On the Role of Space-Time Foam in Breaking Supersymmetry via the Barbero-Immirzi Parameter
• Gravity Asymptotics with Topological Parameters
• Quantum realizations of Hilbert-Palatini second-class constraints
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• The theta parameter in loop quantum gravity: effects on quantum geometry and black hole entropy
• Torsional degrees of freedom in AdS4/CFT3
• Deformed BF theory as a theory of gravity and supergravity
• Mimetic-Metric-Torsion with induced Axial mode and Phantom barrier crossing
• Parity violation in Poincaré gauge gravity
• Quantum-Ordering Ambiguities in Weak Chern-Simons 4D Gravity and Metastability of the Condensate-Induced Inflation
• Modifications in the Spectrum of Primordial Gravitational Waves Induced by Instantonic Fluctuations
• Hamiltonian Analysis of $R+T^2$ Action
• The gauging procedure and carrollian gravity
• Connection dynamics of a gauge theory of gravity coupled with matter
• Induced gauge interactions revisited