Lorentz-covariant Hamiltonian analysis of BF gravity with the Immirzi parameter

@article{Celada2012LorentzcovariantHA,
  title={Lorentz-covariant Hamiltonian analysis of BF gravity with the Immirzi parameter},
  author={Mariano Celada and Merced Montesinos},
  journal={Classical and Quantum Gravity},
  year={2012},
  volume={29}
}
We perform the Lorentz-covariant Hamiltonian analysis of two Lagrangian action principles that describe general relativity as a constrained BF theory and that include the Immirzi parameter. The relation between these two Lagrangian actions has already been studied through a map among the fields involved. The main difference between these is the way the Immirzi parameter is included, since in one of them the Immirzi parameter is included explicitly in the BF terms, whereas in the other (the CMPR… 

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References

SHOWING 1-10 OF 56 REFERENCES

A new look at Lorentz-Covariant Loop Quantum Gravity

In this work, we study the classical and quantum properties of the unique commutative Lorentz-covariant connection for loop quantum gravity. This connection has been found after solving the

Covariant canonical formalism for four-dimensional BF theory

The covariant canonical formalism for four-dimensional BF theory is performed. The aim of the paper is to understand in the context of the covariant canonical formalism both the reducibility that

Loop Quantum Gravity seen from Covariant Theory

Covariant loop gravity comes out of the canonical analysis of the Palatini action and the use of the Dirac brackets arising from dealing with the second class constraints (“simplicity” constraints).

Hamiltonian analysis of non-chiral Plebanski theory and its generalizations

We consider the non-chiral, full Lorentz group-based Plebanski formulation of general relativity in its version that utilizes the Lagrange multiplier field Φ with ‘internal’ indices. The Hamiltonian

A Lorentz-Covariant Connection for Canonical Gravity

We construct a Lorentz-covariant connection in the context of first order cano- nical gravity with non-vanishing Barbero{Immirzi parameter. To do so, we start with the phase space formulation derived

COMMENT ON "DIMENSION OF THE MODULI SPACE AND HAMILTONIAN ANALYSIS OF BF FIELD THEORIES"

The purpose of this Comment is to point out that the results presented in the appendix of M. Mondragon and M. Montesinos, J. Math. Phys.47, 022301 (2006) provides a generic method so as to deal with

SU(2) loop quantum gravity seen from covariant theory

Covariant loop gravity comes out of the canonical analysis of the Palatini action and the use of the Dirac brackets arising from dealing with the second class constraints (“simplicity” constraints).

On choice of connection in loop quantum gravity

We investigate the quantum area operator in the loop approach based on the Lorentz covariant Hamiltonian formulation of general relativity. We show that there exists a two-parameter family of Lorentz

Topological parameters in gravity

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

Four-dimensional Lorentzian Holst action with topological terms

We study the Hamiltonian formulation of the general first order action of general relativity compatible with local Lorentz invariance and background independence. The most general simplectic
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