Related papers: Ashtekar's Variables for Arbitrary Gauge Group
The classical Einstein's gravity can be reformulated from the constrained U(2,2) gauge theory on the ordinary (commutative) four-dimensional spacetime. Here we consider a noncommutative manifold with a symplectic structure and construct a…
A new representation for canonical gravity and supergravity is presented, which combines advantages of Ashtekar's and the Wheeler~DeWitt representation: it has a nice geometric structure and the singular metric problem is absent. A formal…
How to make compatible both boundary and gauge conditions for generally covariant theories using the gauge symmetry generated by first class constraints is studied. This approach employs finite gauge transformations in contrast with…
We present a new approach to the covariant canonical formulation of Einstein-Cartan gravity that preserves the full Lorentz group as the local gauge group. The method exploits lessons learned from gravity in 2+1 dimensions regarding the…
General Relativity is usually formulated as a theory with gauge invariance under the diffeomorphism group, but there is a 'dilaton' formulation where it is in addition invariant under Weyl transformations, and a 'unimodular' formulation…
We show that the recent claim that the 2+1 dimensional Ashtekar formulation for General Relativity has a finite number of physical degrees of freedom is not correct.
The relation between the SL(2,R)/SO(2)- and the SL(2,C)-chiral model that naturally arise within the metric respectively the Ashtekar formulation of two Killing field reduced Einstein gravity is revealed. Both chiral models turn out to be…
The Lagrangian formulation of classical field theories and in particular general relativity leads to a coordinate-free, fully covariant analysis of these constrained systems. This paper applies multisymplectic techniques to obtain the…
Starting from a topological gauge theory in two dimensions with symmetry groups $ISO(2,1)$, $SO(2,1)$ and $SO(1,2)$ we construct a model for gravity with non-trivial coupling to matter. We discuss the equations of motion which are connected…
We formulate a topological theory in six dimensions with gauge group SO(3,3) which reduces to gravity on a four dimensional defect if suitable boundary conditions are chosen. In such a framework we implement the reflection automorphism of…
The method of solution of the initial value constraints for pure canonical gravity in terms of Ashtekar's new canonical variables due to CDJ is further developed in the present paper. There are 2 new main results : 1) We extend the method…
GR can be interpreted as a theory of evolving 3-geometries. A recent such formulation, the 3-space approach of Barbour, Foster and \'{O} Murchadha, also permits the construction of a limited number of other theories of evolving…
We develop worldline formulations of covariant fracton gauge theories. These are a one-parameter family of gauge theories of a rank-two symmetric tensor field, invariant under a scalar gauge transformation involving a double derivative.…
A possible Yang-Mills like lagrangian formulation for gravity is explored. The starting point consists on two next assumptions. First, the metric is assumed as a real map from a given gauge group. Second, a gauge invariant lagrangian…
The framework of the Covariant Canonical Gauge theory of Gravity (CCGG) is described in detail. CCGG emerges naturally in the Palatini formulation, where the vierbein and the spin connection are independent fields. Neither torsion nor…
The present article summarizes the work of the papers \cite{1} dealing with the quantization of pure gravity and gravity coupled to a Maxwell field and a cosmological constant in presence of spherical symmetry. The class of models presented…
It is shown how to write the first order action for gravity in a gauge theoretic formalism where the spin connection and frame field degrees of freedom are assimilated together into a gauge connection. It is then shown how to couple the…
Canonical transformations relating the variables of the ADM-, Ashtekar's and Witten's formulations of gravity are computed in 2+1~dimensions. Three different forms of the BRST-charge are given in the 2+1 dimensional Ashtekar formalism, two…
We discuss linearized gravity from the point of view of a gauge theory. In (3+1)-dimensions our analysis allows to consider linearized gravity in the context of the MacDowell-Mansouri formalism. Our observations may be of particular…
We study the Geroch group in the framework of the Ashtekar formulation. In the case of the one-Killing-vector reduction, it turns out that the third column of the Ashtekar connection is essentially the gradient of the Ernst potential, which…