Related papers: Barbero's formulation from a $BF$-type action with…
The canonical quantization of diffeomorphism invariant theories of connections in terms of loop variables is revisited. Such theories include general relativity described in terms of Ashtekar-Barbero variables and extension to Yang-Mills…
We set up a canonical Hamiltonian formulation for a theory of gravity based on a Lagrangian density made up of the Hilbert-Palatini term and, instead of the Holst term, the Nieh-Yan topological density. The resulting set of constraints in…
We present a parameter-free gauge formulation of general relativity in terms of a new set of real spin connection variables. The theory is constructed by extending the phase space of the recently formulated conformal geometrodynamics for…
We present a histories version of the connection formalism of general relativity. Such an approach introduces a spacetime description--a characteristic feature of the histories approach--and we discuss the extent to which the usual loop…
In this paper we generalise previous work on tensor perturbations in a de Sitter background in terms of Ashtekar variables to cover all complex values of the Immirzi parameter gamma (previous work was restricted to imaginary gamma).…
A generalization of General Relativity is studied. The standard Einstein-Hilbert action is considered in the Palatini formalism, where the connection and the metric are independent variables, and the connection is not symmetric. As a result…
The BRST transformations for gravity in Ashtekar variables are obtained by using the Maurer-Cartan horizontality conditions. The BRST cohomology in Ashtekar variables is calculated with the help of an operator $\delta$ introduced by S.P.…
We consider cosmological solution for Einstein gravity with massive fermions with a four-fermion coupling, which emerges from the Holst action and is related to the Barbero-Immirzi (BI) parameter. This gravitational action is an important…
Canonical quantization of the Brane-World effective action presented by Kanno and Soda containing higher order curvature invariant terms, has been performed. It requires introduction of an auxiliary variable. As observed in a series of…
In this paper it is implemented how to make compatible the boundary conditions and the gauge fixing conditions for complex general relativity written in terms of Ashtekar variables using the Henneaux-Teitelboim-Vergara approach. Moreover,…
In this paper we revisit the canonical analysis of $BF$ gravity with the Immirzi parameter and a cosmological constant. By examining the constraint on the $B$ field, we realize that the analysis can be performed in a Lorentz-covariant…
The Hamiltonian formulation with action-angle variables is very useful when considering the motion of particles undergoing a self-force reaction due to gravitational wave emission. Using the proper time as a parameter along the trajectory…
In a classical theory of gravity, the Barbero-Immirzi parameter ($\eta$) appears as a topological coupling constant through the Lagrangian density containing the Hilbert-Palatini term and the Nieh-Yan invariant. In a quantum framework, the…
A variational framework for the quantization of gravitational fields is developed based on an extension of the stationary action principle. Within this framework, the Wheeler-DeWitt equation for the gravitational wave functional is…
The action of general relativity proposed by Capovilla, Jacobson and Dell is written in terms of $SO(3)$ gauge fields and gives Ashtekar's constraints for Einstein gravity. However, it does not depend on the space-time metric nor its…
We generalize the Lagrangian of N = 1 supergravity (SUGRA) by using an arbitrary parameter $\xi$, which corresponds to the inverse of Barbero's parameter $\beta$. This generalized Lagrangian involves the chiral one as a special case of the…
The Barbero-Immirzi (BI) parameter is promoted to a field and a canonical analysis is performed when it is coupled with a Nieh-Yan topological invariant. It is shown that, in the effective theory, the BI field is a canonical pseudoscalar…
The 1-parameter family of transformations identified by Barbero and Immirzi plays a significant role in non-perturbative approaches to quantum gravity, among them Loop Quantum Gravity and Spin Foams. It facilitates the loop quantization…
Starting from a Hamiltonian description of four dimensional general relativity in presence of a cosmological constant we perform the program of canonical quantisation. This is done using complex Ashtekar variables while keeping the…
An action principle is described which unifies general relativity and topological field theory. An additional degree of freedom is introduced and depending on the value it takes the theory has solutions that reduce it to 1) general…