Concise symplectic formulation for tetrad gravity

Abstract

We discuss a simple symplectic formulation for tetrad gravity that leads to the real Ashtekar variables in a direct and transparent way. It also sheds light on the role of the Immirzi parameter and the time gauge.

arXiv comment5 pages

References in corpus (12)

• Real Ashtekar Variables for Lorentzian Signature Space-times
• Barbero's Hamiltonian derived from a generalized Hilbert-Palatini action
• 4d Lorentzian Holst action with topological terms
• A note on the Holst action, the time gauge, and the Barbero-Immirzi parameter
• The reduced phase space of Palatini-Cartan-Holst theory
• Dirac's algorithm in the presence of boundaries: a practical guide to a geometric approach
• Manifestly Lorentz-covariant variables for the phase space of general relativity
• Canonical analysis of Holst action without second-class constraints
• Generalizations of the Pontryagin and Husain-Kuchař actions to manifolds with boundary
• Towards general relativity through parametrized theories
• Hamiltonian description of the parametrized scalar field in bounded spatial regions
• Hamiltonian dynamics of the parametrized electromagnetic field

Cited by in corpus (9)

• Null infinity as an open Hamiltonian system
• Proof of the equivalence of the symplectic forms derived from the canonical and the covariant phase space formalisms
• Hamiltonian Gotay-Nester-Hinds analysis of the parametrized unimodular extension of the Holst action
• Palatini gravity with nonmetricity, torsion, and boundaries in metric and connection variables
• On the on-shell equivalence of general relativity and Holst theories with nonmetricity, torsion, and boundaries
• Euclidean self-dual gravity: Ashtekar variables without gauge fixing
• Three roads to the geometric constraint formulation of gravitational theories with boundaries
• Consistent and non-consistent deformations of gravitational theories
• Poisson brackets in Sobolev spaces: a mock holonomy-flux algebra