Related papers: From lattice BF gauge theory to area-angle Regge c…

Theory of gravity is considered in the Regge-Teitelboim approach in which the pseudo-Riemannian space is treated as a surface isometrically embedded in an ambient Minkowski space of higher dimension. This approach is formulated in terms of…

We consider the piecewise flat spacetime and a simplicial analog of the Palatini form of the general relativity (GR) action where the discrete Christoffel symbols are given on the tetrahedra as variables that are independent of the metric.…

We consider spinfoam quantum gravity for general triangulations in the regime $l_P^2\ll a\ll a/\gamma$, namely in the combined classical limit of large areas $a$ and flipped limit of small Barbero-Immirzi parameter $\gamma$, where $l_P$ is…

Any approach to pure quantum gravity must eventually face the question of coupling quantum matter to the theory. In the past, several ways of coupling matter to spin foam quantum gravity have been proposed, but the dynamics of the coupled…

The Regge Calculus approximates a continuous manifold by a simplicial lattice, keeping the connectivities of the underlying lattice fixed and taking the edge lengths as degrees of freedom. The Discrete Regge model employed in this work…

We study a simple lattice model with local symmetry, whose construction is based on a crossed module of finite groups. Its dynamical degrees of freedom are associated both to links and faces of a four-dimensional lattice. In special limits…

We study the generalised constrained BF theory described in gr-qc/0102073 in order to introduce the Immirzi parameter in spin foam models. We show that the resulting spin foam model is still based on simple representations and that the…

We propose a new systematic approach that allows one to derive the spin foam (state sum) model of a theory starting from the corresponding classical action functional. It can be applied to any theory whose action can be written as that of…

We show that the degenerate sector of Spin(4) Plebanski formulation of four-dimensional gravity is exactly solvable and describes covariantly embedded SU(2) BF theory. This fact ensures that its spin foam quantization is given by the SU(2)…

We will examine the issue of diffeomorphism symmetry in simplicial models of (quantum) gravity, in particular for Regge calculus. We find that for a solution with curvature there do not exist exact gauge symmetries on the discrete level.…

In Loop Quantum Gravity, tremendous progress has been made using the Ashtekar-Barbero variables. These variables, defined in a gauge-fixing of the theory, correspond to a parametrization of the solutions of the so-called simplicity…

We show that a new symmetry requirement on the GFT field, in the context of an extended GFT formalism, involving both Lie algebra and group elements, leads, in 3d, to Feynman amplitudes with a simplicial path integral form based on the…

Considering our (3+1)-dimensional space-time as, in some way, discrete or l attice with a parameter $a=\lambda_P$, where $\lambda_P$ is the Planck length, we have investigated the additional contributions of lattice artifact monopoles to…

We review the structure of local Lagrangians and field equations for free bosonic and fermionic gauge fields of mixed symmetry in flat space. These are first presented in a constrained setting and then the ($\g$-)trace constraints on fields…

An idea of reality conditions in the context of spin foams (Barrett-Crane models) is developed. The square of areas are the most elementary observables in the case of spin foams. This observation implies that simplest reality conditions in…

We investigate the renormalization group (RG) flow of SU(3) lattice gauge theory in a two coupling space with couplings $\beta_{11}$ and $\beta_{12}$ corresponding to $1\times 1$ and $1\times 2$ loops respectively. Extensive numerical…

In this work, it is demonstrated how the kinematical Hilbert space of Loop Quantum Gravity (LQG) can be inferred from the configuration space of BF theories via the imposition of the Hamiltonian constraints. In particular, it is outlined…

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…

Dynamical generation of 4d gauge theories and gravity at low energy from the 3d ones at high energy is studied, based on the fermion condensation mechanism recently proposed by Arkani-Hamed, Cohen and Georgi. For gravity, 4d Einstein…

We present an interpretation of loop quantization in the framework of lattice gauge theory. Within this context the lack of appropriate notions of effective theories and renormalization group flow exhibit loop quantization as an incomplete…