Related papers: Phase space descriptions for simplicial 4d geometr…
We demonstrate a tensor renormalization group (TRG) calculation for a two-dimensional Lorentzian model of quantum Regge calculus (QRC). This model is expressed in terms of a tensor network by discretizing the continuous edge lengths of…
Group Field Theories, a generalization of matrix models for 2d gravity, represent a 2nd quantization of both loop quantum gravity and simplicial quantum gravity. In this paper, we construct a new class of Group Field Theory models, for any…
Two sets of spatially diffeomorphism invariant operators are constructed in the loop representation formulation of quantum gravity. This is done by coupling general relativity to an anti- symmetric tensor gauge field and using that field to…
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…
Two-dimensional random surfaces are studied numerically by the dynamical triangulation method. In order to generate various kinds of random surfaces, two higher derivative terms are added to the action. The phases of surfaces in the…
By restricting the functional integration to the Regge geometries, we give the discretized version of the well known path integral formulation of 2--dimensional quantum gravity in the conformal gauge. We analyze the role played by…
In order to test the canonical quantization programme for general relativity we introduce a reduced model for a real sector of complexified Ashtekar gravity which captures important properties of the full theory. While it does not…
In this work we discuss the construction of "simplicial BF theory", the field theory with finite-dimensional space of fields, associated to a triangulated manifold, that is in a sense equivalent to topological BF theory on the manifold…
We present evidence that a nonperturbative model of quantum gravity defined via Euclidean dynamical triangulations contains a region in parameter space with an extended 4-dimensional geometry when a non-trivial measure term is included in…
The 1-parameter family of transformations identified by Barbero and Immirzi plays a significant role in non-perturbative approaches to quantum gravity, among them Loop Quantum Gravity and Spin Foams. It facilitates the loop quantization…
The phase diagram of 2d Lorentzian quantum gravity (LQG) coupled to conformal matter is studied. A phase transition is observed at $c=c_{\rm crit}$ ($1/2<c_{\rm crit}<4$) which can be thought of as the analogue of the $c=1$ barrier of…
The method of four-dimensional Causal Dynamical Triangulations provides a background-independent definition of the sum over geometries in quantum gravity, in the presence of a positive cosmological constant. We present the evidence…
To clarify the geometric information encoded in the $SO(D+1)$ spin-network states for the higher dimensional loop quantum gravity, we generalize the twisted-geometry parametrization of the $SU(2)$ phase space for $(1+3)$ dimensional loop…
Phase space is the state space of classical mechanics, and this manifold is normally endowed only with a symplectic form. The geometry of quantum mechanics is necessarily more complicated. Arguments will be given to show that augmenting the…
We perform a Hamiltonian reduction of spherically symmetric Einstein gravity with a thin dust shell of positive rest mass. Three spatial topologies are considered: Euclidean (R^3), Kruskal (S^2 x R), and the spatial topology of a…
Recent work on state sum models of quantum gravity in 3 and 4 dimensions has led to interest in the `quantum tetrahedron'. Starting with a classical phase space whose points correspond to geometries of the tetrahedron in R^3, we use…
We review the relation between Loop Quantum Gravity on a fixed graph and discrete models of gravity. We compare Regge and twisted geometries, and discuss discrete actions based on twisted geometries and on the discretization of the…
We present a formulation of Regge Calculus where arbitrary coordinates are associated to each vertex of a simplicial complex and the degrees of freedom are given by the metric on each simplex. The lengths of the edges are thus determined…
Firstly, we present a reformulation of the standard canonical approach to spherically symmetric systems in which the radial gauge is imposed. This is done via the gauge unfixing technique, which serves as the exposition in the context of…
The dynamical triangulations approach to quantum gravity is investigated in detail for the first time in five dimensions. In this case, the most general action that is linear in components of the f-vector has three terms. It was suspected…