Related papers: Revisiting loop quantum gravity with selfdual vari…
The Plebanski formulation of complex general relativity is given in terms of variables valued in the complexification of the $so(3)$ Lie algebra. Therefore, it is genuinely a gauge theory that is also diffeomorphism-invariant. For this…
The field equations of noncommutative gravity can be obtained by replacing all exterior products by twist-deformed exterior products in the action functional of general relativity, and are here studied by requiring that the torsion 2-form…
We show that the canonical formulation of a generic action for 1+1-dimensional models of gravity coupled to matter admits a description in terms of Ashtekar-type variables. This includes the CGHS model and spherically symmetric reductions…
The existing approaches to quantization of gravity aim at giving quantum description of 3-geometry following to the ideas of the Wheeler -- DeWitt geometrodynamics. In this description the role of gauge gravitational degrees of freedom is…
I show in this letter that it is possible to construct a Hamiltonian description for Lorentzian General Relativity in terms of two real $SO(3)$ connections. The constraints are simple polynomials in the basic variables. The present…
We examine one of the advantages of Ashtekar's formulation of general relativity: a tractability of degenerate points from the point of view of following the dynamics of classical spacetime. Assuming that all dynamical variables are finite,…
To write down a path integral for the Ashtekar gravity one must solve three fundamental problems. First, one must understand rules of complex contour functional integration with holomorphic action. Second, one should find which gauges are…
We carry out the canonical analysis of the $n$-dimensional Palatini action with or without a cosmological constant $(n\geq3)$ introducing neither second-class constraints nor resorting to any gauge fixing. This is accomplished by providing…
Unitarity is a difficult concept to implement in canonical quantum gravity because of state non-normalizability and the problem of time. We take a realist approach based on pilot-wave theory to address this issue in the Ashtekar formulation…
A starting point for the present work was the statement recently discussed in the literature that two Hamiltonian formulations for the theory of gravity, the one proposed by Dirac and the other by Arnowitt - Deser - Misner, may not be…
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…
In this and a companion paper, we show that quantum field theories with gauge symmetries permit a broader class of classical dynamics than typically assumed. In this article, we show that the dynamics extracted from the path integral or…
We study the phase space structure of the Jackiw-Teitelboim model in its connection variables formulation where the gauge group of the field theory is given by local SL(2,R) (or SU(2) for the Euclidean model), i.e. the de Sitter group in…
Scalar cosmological perturbations in loop quantum cosmology (LQC) is revisited in a covariant manner, using self dual Ashtekar variables. For real-valued Ashtekar-Barbero variables, this `deformed algebra' approach has been shown to…
The general relativity theory is redefined equivalently in almost Kahler variables: symplectic form and canonical symplectic connection (distorted from the Levi-Civita connection by a tensor constructed only from metric coefficients and…
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…
The preceding talks given at this conference have dealt mainly with general ideas for, main problems of and techniques for the task of quantizing gravity canonically. Since one of the major motivations to arrange for this meeting was that…
We explore the cosmological viability of a theory of gravity defined by the Lagrangian $f(\mathcal{R})=\mathcal{R}^{n\left(\mathcal{R}\right)}$ in the Palatini formalism, where $n\left(\mathcal{R}\right)$ is a dimensionless function of the…
Shape dynamics is a reformulation of general relativity, locally equivalent to Einstein's theory, in which the refoliation invariance of the older theory is traded for local scale invariance. Shape dynamics is here derived in a formulation…
Looking for a quantum-mechanical implementation of duality, we formulate a relation between coherent states and complex-differentiable structures on classical phase space ${\cal C}$. A necessary and sufficient condition for the existence of…