Topological parameters in gravity

Abstract

We present the Hamiltonian analysis of the theory of gravity based on a Lagrangian density containing Hilbert-Palatini term along with three topological densities, Nieh-Yan, Pontryagin and Euler. The addition of these topological terms modifies the symplectic structure non-trivially. The resulting canonical theory develops a dependence on three parameters which are coefficients of these terms. In the time gauge, we obtain a real SU (2) gauge theoretic description with a set of seven first class constraints corresponding to three SU (2) rotations, three spatial diffeomorphism and one to evolution in a timelike direction. Inverse of the coefficient of Nieh-Yan term, identified as Barbero-Immirzi parameter, acts as the coupling constant of the gauge theory.

references added

References in corpus (4)

• Beyond Einstein-Cartan gravity: Quadratic torsion and curvature invariants with even and odd parity including all boundary terms
• Topological Interpretation of Barbero-Immirzi Parameter
• From the Einstein-Cartan to the Ashtekar-Barbero canonical constraints, passing through the Nieh-Yan functional
• Holst Actions for Supergravity Theories

Cited by in corpus (20)

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• SU(2) gauge theory of gravity with topological invariants
• Matter in Loop Quantum Gravity
• Torsional instanton effects in quantum gravity
• Generalizations of the Nieh-Yan topological invariant
• Vector-tensor gravity from a broken gauge symmetry
• A discrete discontinuity between the two phases of gravity
• Dark Energy from Topology
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• Revisiting canonical gravity with fermions
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• Modified Compton Effect and CMB Anisotropy
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