Related papers: Regge calculus from a new angle
In the lattice approach to Loop Quantum Gravity on a fixed graph computations tend to be involved and are rarely analytically manageable. But, when interested in the expectation values of coherent states on the lattice which are sharply…
We review how reparametrization of space and time, namely the procedure where both are made to depend on yet another parameter, can be used to formulate quantum physics in a way that is naturally conducive to relativity. This leads us to a…
A new lattice based scheme for numerical relativity will be presented. The scheme uses the same data as would be used in the Regge calculus (eg. a set of leg lengths on a simplicial lattice) but it differs significantly in the way that the…
We describe the idea of studying quantum gravity by means of dynamical triangulations and give examples of its implementation in 2, 3 and 4 space time dimensions. For $d=2$ we consider the generic hermitian 1-matrix model. We introduce the…
We will ask the question of whether or not the Regge calculus (and two related simplicial formulations) is a consistent approximation to General Relativity. Our criteria will be based on the behaviour of residual errors in the discrete…
The recently introduced consistent discrete lattice formulation of canonical general relativity produces a discrete theory that is constraint-free. This immediately allows to overcome several of the traditional obstacles posed by the…
The late universe's matter distribution obeys the Copernican principle at only the coarsest of scales. The relative importance of such inhomogeneity is still not well understood. Because of the Einstein field equations' non-linear nature,…
The problem of time and the quantization of three dimensional gravity in the strong coupling regime is studied following path integral methods. The time is identified with the volume of spacetime. We show that the effective action describes…
Regge calculus is a powerful method to approximate 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…
In this paper, we study the discrete classical phase space of loop gravity, which is expressed in terms of the holonomy-flux variables, and show how it is related to the continuous phase space of general relativity. In particular, we prove…
The 4-dimensional space-time is extended to pseudo-complex coordinates. Proposing the standard quantization rules in this extended space, the ones for the 4-dimensional sub-space acquire, as one solution, the commutation relations with…
A key insight used in developing the theory of Causal Dynamical Triangulations (CDTs) is to use the causal (or light-cone) structure of Lorentzian manifolds to restrict the class of geometries appearing in the Quantum Gravity (QG) path…
Present-day quantum field theory can be regularized by a decomposition into quantum simplices. This replaces the infinite-dimensional Hilbert space by a high-dimensional spinor space and singular canonical Lie groups by regular spin groups.…
We present a novel solution to the cosmological constant (CC) problem that requires no fine-tunings nor anthropic reasoning. In pre-geometric gravity (PGG), spacetime emerges from the spontaneous breaking of a fundamental gauge symmetry.…
We consider two versions of quantum Regge calculus. The Standard Regge Calculus where the quadratic link lengths of the simplicial manifold vary continuously and the Z_2-Regge Model where they are restricted to two possible values. The goal…
Four-dimensional simplicial quantum gravity is modified either by coupling it to U(1) gauge fields or by introducing a measure weighted by the orders of the triangles. Strong coupling expansion and Monte Carlo simulations are used. Although…
Causal Dynamical Triangulations (CDT) is a methodology to define and compute the gravitational path integral, whose aim is a fully fledged nonperturbative quantum field theory of gravity and spacetime. Analogous to lattice formulations of…
In this contribution, we study spacetimes of cosmological interest, without making any symmetry assumptions. We prove a rigid Hawking singularity theorem for positive cosmological constant, which sharpens known results. In particular, it…
It has been shown that if one solves self-consistently the semiclassical Einstein equations in the presence of a quantum scalar field, with a cutoff on the number of modes, spacetime become flatter when the cutoff increases. Here we extend…
The 3-space of a universe model is defined at a certain simultaneity. Hence space depends on which time is used. We find a general formula generating all known and also some new transformations to conformally flat spacetime coordinates. A…