Related papers: Homogeneous 2+1 Dimensional Gravity in the Ashteka…
A generally covariant gauge theory for an arbitrary gauge group with dimension $\geq 3$, that reduces to Ashtekar's canonical formulation of gravity for SO(3,C), is presented. The canonical form of the theory is shown to contain only first…
Superspace parametrized by gauge potentials instead of metric three-geometries is discussed in the context of the Ashtekar variables. Among other things, an "internal clock" for the full theory can be identified. Gauge-fixing conditions…
In terms of Dirac matrices the self-dual and anti-self-dual decomposition of a conformal supergravity is given and a self-dual conformal supergravity theory is developed as a connection dynamic theory in which the basic dynamic variabes…
Quantum deformations of (anti-)de Sitter algebras in (2+1) dimensions are revisited, and several features of these quantum structures are reviewed. In particular, the classification problem of (2+1) (A)dS Lie bialgebras is presented and the…
The usual description of 2+1 dimensional Einstein gravity as a Chern-Simons (CS) theory is extended to a one parameter family of descriptions of 2+1 Einstein gravity. This is done by replacing the Poincare' gauge group symmetry by a…
The manuscript studies a 3+N+1-dimensional space in which the N extra dimensions are dynamically compact. The 3 large dimensions, behaving as the spacial part of the FRW metric, possess a different scale factor in comparison with the N…
This work addresses a specific technical question of relevance to canonical quantization of gravity using the so-called new variables and loop-based techniques of Ashtekar, Rovelli, and Smolin. In particular, certain `superselection laws'…
$[n+1]$-dimensional ($n\geq 3$) smooth Einsteinian spaces of Euclidean and Lorentzian signature are considered. The base manifold $M$ is supposed to be smoothly foliated by a two-parameter family of codimension-two-surfaces which are…
We consider the formulation of entropic gravity in two spacetime dimensions. The usual gravitational force law is derived even in the absence of area, as normally required by the holographic principle. A special feature of this perspective…
One of the virtues of the Ashtekar variables is the simplification of the initial value constraints for gravity. In the case of self-dual variables this entails a complexification of the phase space which comes at the expense of having to…
As basic variables in general relativity (GR) are chosen antisymmetric connection and bivectors - bilinear in tetrad area tensors subject to appropriate (bilinear) constraints. In canonical formalism we get theory with polinomial…
We generate new 11-dimensional supergravity solutions from deformations based on U(1)^3 symmetries. The initial geometries are of the form AdS_4 x Y_7, where Y_7 is a 7-dimensional Sasaki-Einstein space. We consider a general family of…
The 3+1 (canonical) decomposition of all geometries admitting two-dimensional space-like surfaces is exhibited. A proposal consisting of a specific re-normalization {\bf Assumption} and an accompanying {\bf Requirement} is put forward,…
In the context of the formalism proposed by Stelle-West and Grignani-Nardelli, it is shown that Chern-Simons supergravity can be consistently obtained as a dimensional reduction of (3+1)-dimensional supergravity, when written as a gauge…
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.…
Several investigations in the study of cosmological structure formation use numerical simulations in both two and three dimensions. In this paper we address the subtle question of ambiguities in the nature of two dimensional gravity in an…
We give an SU(2) covariant representation of the constraints of Euclidean general relativity in the Ashtekar variables. The guiding principle is the use of triads to transform all free spatial indices into SU(2) indices. A central role is…
An inhomogeneous (1+1)-dimensional model of the quantum gravity is considered. It is found, that this model corresponds to a string propagating against some curved background space. The quantization scheme including the Wheeler-DeWitt…
Using self dual Ashtekar variables, we investigate (at the effective level) the spherically symmetry reduced model of loop quantum gravity, both in vacuum and when coupled to a scalar field. Within the real Ashtekar-Barbero formulation, the…
Inspired by problems arising in the geometrical treatment of Yang-Mills theories and Palatini's gravity, the covariant formulation of Hamiltonian dynamical systems as a Hamiltonian field theory of dimension $1+0$ on a manifold with boundary…