Reality conditions for Ashtekar gravity from Lorentz-covariant formulation

Abstract

We show the equivalence of the Lorentz-covariant canonical formulation considered for the Immirzi parameter $\beta =i$ to the selfdual Ashtekar gravity. We also propose to deal with the reality conditions in terms of Dirac brackets derived from the covariant formulation and defined on an extended phase space which involves, besides the selfdual variables, also their anti-selfdual counterparts.

14 pages

References in corpus (1)

• Timelike surfaces in Lorentz covariant loop gravity and spin foam models

Cited by in corpus (19)

• The Spin Foam Approach to Quantum Gravity
• Fermions in Ashtekar-Barbero Connections Formalism for Arbitrary Values of the Immirzi Parameter
• Simplicity in simplicial phase space
• 4d Lorentzian Holst action with topological terms
• The twistorial structure of loop-gravity transition amplitudes
• Simplicity and closure constraints in spin foam models of gravity
• Complex Ashtekar variables and reality conditions for Holst's action
• Critical Overview of Loops and Foams
• Canonical structure of Tetrad Bimetric Gravity
• First order gravity on the light front
• The phase structure of Einstein-Cartan theory
• Detailed discussions and calculations of quantum Regge calculus of Einstein-Cartan theory
• Hamiltonian spinfoam gravity
• Hamiltonian Gotay-Nester-Hinds analysis of the parametrized unimodular extension of the Holst action
• The new spin foam models and quantum gravity
• Poincare-Plebanski formulation of GR and dual simplicity constraints
• Towards self dual Loop Quantum Gravity
• Canonical structure of minimal varying $\Lambda$ theories
• Simplicity constraints: a 3d toy-model for Loop Quantum Gravity