Related papers: Deformed Spinor Networks for Loop Gravity: Towards…
We develop a two-dimensional gravity path integral formulation of the $T \bar T + \Lambda_2$ deformation of quantum field theory. This provides an exactly solvable generalization of the pure $T \bar T$ deformation that is relevant for de…
Non-perturbative approaches to quantum gravity call for a deep understanding of the emergence of geometry and locality from the quantum state of the gravitational field. Without background geometry, the notion of distance should entirely…
In this paper we point out some possible links between different approaches to quantum gravity and theories of the Planck scale physics. In particular, connections between Loop Quantum Gravity, Causal Dynamical Triangulations,…
We consider the quantization of gravity as an SL(2,C) gauge theory in terms of Ashtekar's selfdual variables and reality conditions for the spatial metric (RCI) and its evolution (RCII). We start from a holomorphic phase space formulation.…
Loop quantum gravity corrections, in the presence of inhomogeneities, can lead to a deformed constraint algebra. Such a deformation implies that the effective theory is no longer generally covariant. As a consequence, the geometrical…
After a brief review of spin networks and their interpretation as wave functions for the (space) geometry, we discuss the renormalisation of the area operator in loop quantum gravity. In such a background independent framework, we propose…
In recent years, a close connection between supergravity, string effective actions and generalized geometry has been discovered that typically involves a doubling of geometric structures. We investigate this relation from the point of view…
We develop a new perspective on the discretization of the phase space structure of gravity in 2+1 dimensions as a piecewise-flat geometry in 2 spatial dimensions. Starting from a subdivision of the continuum geometric and phase space…
The building blocks of a quantum theory of general relativity are expected to be discrete structures. Loop quantum gravity is formulated using a basis of spin networks (wave functions over oriented graphs with coloured edges), thus…
Different versions of consistent canonical realizations of hypersurface deformations of spherically symmetric space-times have been derived in models of loop quantum gravity, modifying the classical dynamics and sometimes also the structure…
Vielbeins are necessary when coupling General Relativity (GR) to fermionic matter. This enhances the gauge group of GR to include local Lorentz transformations. In view of a reduced phase space formulation of quantum gravity, in this work…
We perform a rigorous piecewise-flat discretization of classical general relativity in the first-order formulation, in both 2+1 and 3+1 dimensions, carefully keeping track of curvature and torsion via holonomies. We show that the resulting…
In this article we introduce a new operator representing the three-dimensional scalar curvature in loop quantum gravity. Our construction does not apply to the entire kinematical Hilbert space of loop quantum gravity; instead, the operator…
Spin networks are at the core of quantum gravity. Our aim is to plug the mathematical community at large into the procedures turn to create a finite quantum theory of general relativity. For this, because of the different cultural…
Motivated by the two-dimensional massive gravity description of $T\overline{T}$ deformations, we propose a direct generalization in $d$ dimensions. Our methodology indicates that all terms up to order $d$ are present in the deformation. In…
Loop quantum gravity has provided us with a canonical framework especially devised for background independent and diffeomorphism invariant gauge field theories. In this quantization the fundamental excitations are called spin network…
We study the symplectic reduction of the phase space of two twistors to the cotangent bundle of the Lorentz group. We provide expressions for the Lorentz generators and group elements in terms of the spinors defining the twistors. We use…
We present a generalization of the spinor and twistor geometry for on (pseudo) Riemannian manifolds enabled with nonholonomic distributions or for Finsler-Cartan spaces modelled on tangent Lorentz bundles. Nonholonomic (Finsler) twistors…
Linear spinor fields are a generalization of the Dirac field that have transparent cluster decomposability properties needed for classical correspondence of relativistic quantum systems. The algebra of these fields directly incorporate…
The twisted geometries of spin network states are described by simple twistors, isomorphic to null twistors with a time-like direction singled out. The isomorphism depends on the Immirzi parameter, and reduces to the identity when the…