Related papers: Polyhedra in loop quantum gravity

I review the formalism of loop quantum gravity, in both its real and complex formulations, and spin foam theory which is its path integral counterpart. Spin networks for non-compact groups are introduced (following hep-th/0205268) to deal…

The standard (Berezin-Toeplitz) geometric quantization of a compact Kaehler manifold is restricted by integrality conditions. These restrictions can be circumvented by passing to the universal covering space, provided that the lift of the…

As a laboratory for loop quantum gravity, we consider the canonical quantization of the three-dimensional Chern-Simons theory on a noncompact space with the topology of a cylinder. Working within the loop quantization formalism, we define…

Magnetic systems with frustration often have large classical degeneracy. We show that their low-energy physics can be understood as dynamics within the space of classical ground states. We demonstrate this mapping in a family of quantum…

A generalized Clifford manifold is proposed in which there are coordinates not only for the basis vector generators, but for each element of the Clifford group, including the identity scalar. These new quantities are physically interpreted…

We show that loop gravity can equally well be formulated in in terms of spinorial variables (instead of the group variables which are commonly used), which have recently been shown to provide a direct link between spin network states and…

We review our recent proposal of a method to extend the quantization of spherically symmetric isolated horizons, a seminal result of loop quantum gravity, to a phase space containing horizons of arbitrary geometry. Although the details of…

Isolated horizons model equilibrium states of classical black holes. A detailed quantization, starting from a classical phase space restricted to spherically symmetric horizons, exists in the literature and has since been extended to…

A hyperk\"ahler manifold $M$ has a family of induced complex structures indexed by a two-dimensional sphere $S^2 \cong \mathbb{CP}^1$. The twistor space of $M$ is a complex manifold $Tw(M)$ together with a natural holomorphic projection…

Polymer quantization is as a useful toy model for the mathematical aspects of loop quantum gravity and is interesting in its own right. Analyzing entropies of physically equivalent states in the standard Hilbert space and the polymer…

Spin networks in Loop Quantum Gravity are traditionally described by unitary holonomies corresponding to noiseless transformations. In this work, we extend this framework to incorporate general quantum channels that model effects of…

This is the first paper in a series devoted to understanding the classical and quantum nature of edge modes and symmetries in gravitational systems. The goal of this analysis is to: i) achieve a clear understanding of how different…

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…

We summarize the basics of the loop representation of quantum gravity and describe the main aspects of the formalism, including its latest developments, in a reorganized and consistent form. Recoupling theory, in its graphical…

It is well known that the SU(2)-gauge invariant phase space of loop gravity can be represented in terms of twisted geometries. These are piecewise-linear-flat geometries obtained by gluing together polyhedra, but the resulting geometries…

Let $n$ be any natural number. Let $K$ be any $n$-dimensional knot in $S^{n+2}$. We define a supersymmetric quantum system for $K$ with the following properties. We firstly construct a set of functional spaces (spaces of fermionic \{resp.…

In the context of loop quantum gravity, quantum states of geometry are mathematically defined as spin networks living on graphs embedded in the canonical space-like hypersurface. In the effort to study the renormalisation flow of loop…

This work introduces a new space $\T'_*$ of `vertex-smooth' states for use in the loop approach to quantum gravity. Such states provide a natural domain for Euclidean Hamiltonian constraint operators of the type introduced by Thiemann (and…

The canonical ``loop'' formulation of quantum gravity is a mathematically well defined, background independent, non perturbative standard quantization of Einstein's theory of General Relativity. Some among the most meaningful results of the…

In this paper, I emphasize those features of the extended phase space approach to quantization of gravity that distinguish it among other approaches. First of all, it is the conjecture about non-trivial topology of the Universe which was…