Plebanski Theory and Covariant Canonical Formulation

Abstract

We establish an equivalence between the Hamiltonian formulation of the Plebanski action for general relativity and the covariant canonical formulation of the Hilbert-Palatini action. This is done by comparing the symplectic structures of the two theories through the computation of Dirac brackets. We also construct a shifted connection with simplified Dirac brackets, playing an important role in the covariant loop quantization program, in the Plebanski framework. Implications for spin foam models are also discussed.

18 pages

References in corpus (23)

• Discreteness of area and volume in quantum gravity
• Quantum Theory of Gravity I: Area Operators
• Barbero's Hamiltonian derived from a generalized Hilbert-Palatini action
• Spin Foam Models for Quantum Gravity
• Relativistic spin networks and quantum gravity
• ``Sum over Surfaces'' form of Loop Quantum Gravity
• Quantum Gravity and Regge Calculus
• A Lorentzian Signature Model for Quantum General Relativity
• Spacetime geometry from algebra: spin foam models for non-perturbative quantum gravity
• so(4) Plebanski Action and Relativistic Spin Foam Model
• Gauge transformations in the Lagrangian and Hamiltonian formalisms of generally covariant theories
• SU(2) Loop Quantum Gravity seen from Covariant Theory
• SO(4,C)-covariant Ashtekar-Barbero gravity and the Immirzi parameter
• Hamiltonian Analysis of Plebanski Theory
• On choice of connection in loop quantum gravity
• Area spectrum in Lorentz covariant loop gravity
• BF gravity and the Immirzi parameter
• Barrett-Crane spin foam model from generalized BF-type action for gravity
• Hilbert space structure of covariant loop quantum gravity
• Rigid and gauge Noether symmetries for constrained systems
• Timelike surfaces in Lorentz covariant loop gravity and spin foam models
• Gauge group and reality conditions in Ashtekar's complex formulation of canonical gravity
• Towards a Covariant Loop Quantum Gravity

Cited by in corpus (28)

• The Spin Foam Approach to Quantum Gravity
• Edge modes of gravity -- I: Corner potentials and charges
• Phase space descriptions for simplicial 4d geometries
• Group field theory and simplicial gravity path integrals: A model for Holst-Plebanski gravity
• Edge modes of gravity -- II: Corner metric and Lorentz charges
• Edge modes of gravity. Part III. Corner simplicity constraints
• Spin Foams and Canonical Quantization
• Simplicity in simplicial phase space
• From covariant to canonical formulations of discrete gravity
• Spin foam model from canonical quantization
• The new vertices and canonical quantization
• $BF$ gravity
• Simplicity and closure constraints in spin foam models of gravity
• Discrete Gravity Models and Loop Quantum Gravity: a Short Review
• Critical Overview of Loops and Foams
• Hamiltonian Analysis of non-chiral Plebanski Theory and its Generalizations
• On the role of the Barbero-Immirzi parameter in discrete quantum gravity
• Chiral description of ghost-free massive gravity
• On the Relations between Gravity and BF Theories
• Revisiting the Simplicity Constraints and Coherent Intertwiners
• Null twisted geometries
• Diffeomorphism symmetry in quantum gravity models
• Group field theory and simplicial quantum gravity
• The new spin foam models and quantum gravity
• A Short and Subjective Introduction to the Spinfoam Framework for Quantum Gravity
• Degenerate Plebanski Sector and Spin Foam Quantization
• A pure connection formulation with real fields for Gravity
• Gravitational quantum states as finite representations of the Lorentz group