Related papers: 4-dimensional Spin-foam Model with Quantum Lorentz…

The graphical calculus method is generalized to study the relation between covariant and canonical dynamics of loop quantum gravity. On one hand, a graphical derivation of the partition function of the generalized Euclidean…

In order to avoid the difficulties encountered by relativistic quantum theory of single particles, we pursue a deductive development of the theory from physical principles, without canonical quantization, by making use of group-theoretical…

We present a spin foam model in which the fundamental ``bubble amplitudes'' (the analog of the one-loop corrections in quantum field theory) are finite as the cutoff is removed. The model is a natural variant of the field theoretical…

A manifestly Lorentz-covariant formulation of Loop Quantum Gravity (LQG) is given in terms of finite-dimensional representations of the Lorentz group. The formulation accounts for discrete symmetries, such as parity and time-reversal, and…

The simplicial framework of Engle-Pereira-Rovelli-Livine spin-foam models is generalized to match the diffeomorphism invariant framework of loop quantum gravity. The simplicial spin-foams are generalized to arbitrary linear 2-cell…

Just as 3d state sum models, including 3d quantum gravity, can be built using categories of group representations, "2-categories of 2-group representations" may provide interesting state sum models for 4d quantum topology, if not quantum…

In this work we show that the spin pendulum techniques developed by the E\:{o}t-Wash group could be used to put very stringent bounds on the free parameters of a Lorentz invariant phenomenological model of quantum gravity. The model is…

We construct a class of spin foam models describing matter coupled to gravity, such that the gravitational sector is described by the unitary irreducible representations of the appropriate symmetry group, while the matter sector is…

We propose an explicit spin-foam amplitude for Lorentzian gravity in three dimensions, allowing for both space- and time-like boundaries. The model is based on two main requirements: that it should be structurally similar to its well-known…

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…

We examine the four dimensional path integral for Euclidean quantum gravity in the context of the EPRL-FK spin foam model. The state sum is restricted to certain symmetric configurations which resembles the geometry of a flat homogeneous…

Starting from Ooguri's construction for $BF$ theory in three (and four) dimensions, we show how to construct a well defined theory with an infinite number of degrees of freedom. The spin network states that are kept invariant by the…

In the search for a covariant formulation for Loop Quantum Gravity, spin foams have arised as the corresponding discrete space-time structure and, among the different models, the Barrett-Crane model seems the most promising. Here, we study…

This series of lectures gives a simple and self-contained introduction to the non-perturbative and background independent loop approach of canonical quantum gravity. The Hilbert space of kinematical quantum states is constructed and a…

Spinfoams provide a framework for the dynamics of loop quantum gravity that is manifestly covariant under the full four-dimensional diffeomorphism symmetry group of general relativity. In this way they complete the ideal of…

We study perturbation theory for spin foam models on triangulated manifolds. Starting with any model of this sort, we consider an arbitrary perturbation of the vertex amplitudes, and write the evolution operators of the perturbed model as…

We describe a class of spin foam models of four-dimensional quantum gravity which is based on the integration of the tetrad one-forms in the path integral for the Palatini action of General Relativity. In the Euclidian gravity case this…

Spin foam models, an approach to defining the dynamics of loop quantum gravity, make use of the Plebanski formulation of gravity, in which gravity is recovered from a topological field theory via certain constraints called simplicity…

Starting from the defining transformations of complex matrices for the $SO(4,R)$ group, we construct the fundamental representation and the tensor and spinor representations of the group $SO(4,R)$. Given the commutation relations for the…

We find a quantum group structure in two-dimensional motions of a nonrelativistic electron in a uniform magnetic field and in a periodic potential. The representation basis of the quantum algebra is composed of wavefunctions of the system.…