Related papers: Deformation Quantisation of Gravity
We describe gauge theories which allow to retrieve a large class of gravitational theories, including, MacDowell-Mansouri gravity and its topological extension to Loop Quantum Gravity via the Pontrjagin characteristic class involving the…
We consider the ADM formalism as a tool to build bouncing cosmologies. In this approach, the foliation of the spacetime has to be fixed in order to go beyond General Relativity modifying the gravitational sector. Once a preferred slicing,…
The constraint hypersurfaces defining the Witten and Ashtekar formulations for 2+1 gravity are very different. In particular the constraint hypersurface in the Ashtekar case is not a manifold but consists of several sectors that intersect…
We find the most general solution to Chern-Simons AdS$_3$ gravity in Fefferman-Graham gauge. The connections are equivalent to geometries that have a non-trivial curved boundary, characterized by a 2-dimensional vielbein and a spin…
We review some aspects of three-dimensional quantum gravity with emphasis in the `CFT -> Geometry' map that follows from the Brown-Henneaux conformal algebra. The general solution to the classical equations of motion with anti-de Sitter…
An approach to the quantization of gravity in the presence matter is examined which starts from the classical Einstein-Hilbert action and matter approximated by "point" particles minimally coupled to the metric. Upon quantization, the…
The description of the $T\bar{T}$ deformation in terms of two-dimensional gravity is analyzed from the Hamiltonian point of view, in a manner analogous to the ADM description of general relativity. We find that the Hamiltonian constraints…
We use the mathematical framework of loop quantum gravity (LQG) to study the quantization of three dimensional (Riemannian) gravity with positive cosmological constant (Lambda>0). We show that the usual regularization techniques (successful…
The tomographic representation of quantum fields within the deformation quantization formalism is constructed. By employing the Wigner functional we obtain the symplectic tomogram associated with quantum fields. In addition, the tomographic…
Bimetric variational formalism was recently employed to construct novel bimetric gravity models. In these models an affine connection is generated by an additional tensor field which is independent of the physical metric. In this work we…
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…
It is well known that gravity in 2+1 dimensions can be recast as Chern-Simons theory, with the gauge group given by the local isometry group, depending on the metric signature and the cosmological constant. Point particles are added into…
Anomalies in Yang-Mills type gauge theories of gravity are reviewed. Particular attention is paid to the relation between the Dirac spin, the axial current j_5 and the non-covariant gauge spin C. Using diagrammatic techniques, we show that…
The $q$-deformed loop gravity framework was introduced as a canonical formalism for the Turaev-Viro model (with $\Lambda < 0$), allowing to quantize 3D Euclidean gravity with a (negative) cosmological constant using a quantum deformation of…
It is commonly accepted that the study of 2+1 dimensional quantum gravity could teach us something about the 3+1 dimensional case. The non-perturbative methods developed in this case share, as basic ingredient, a reformulation of gravity as…
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 holographic duality can be extended to include quantum theories with broken coordinate invariance leading to the appearance of the gravitational anomalies. On the gravity side one adds the gravitational Chern-Simons term to the bulk…
The model of nonrelativistic particles coupled to nonstandard (2+1)-gravity [1] is extended to include Abelian or non-Abelian charges coupled to Chern-Simons gauge fields. Equivalently, the model may be viewed as describing the (Abelian or…
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…
We study a type of geometric theory with a non-dynamical one-form field. Its dynamical variables are an $su(2)$ gauge field and a triad of $su(2)$ valued one-forms. Hamiltonian decomposition reveals that the theory has a true Hamiltonian,…