相关论文: Consistent discretization and canonical classical …

The 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 these lecture notes, I describe the motivation behind a recent formulation of a non-perturbative gravitational path integral for Lorentzian (instead of the usual Euclidean) space-times, and give a pedagogical introduction to its main…

In the recently introduced gauge theory of translations, dubbed Coincident General Relativity, gravity is described with neither torsion nor curvature in the spacetime affine geometry. The action of the theory enjoys an enhanced symmetry…

Discretization of general relativity is a promising route towards quantum gravity. Discrete geometries have a finite number of degrees of freedom and can mimic aspects of quantum geometry. However, selection of the correct discrete freedoms…

Simplicial approaches to quantum gravity such as quantum Regge calculus and spin foams include configurations where bulk edges can become arbitrarily large while the boundary edges are kept small. Spikes and spines are prime examples for…

We give an explicit form for the Lorentzian vertices recently introduced for possibly defining the dynamics of loop quantum gravity. As a result of so doing, a natural regularization of the vertices is suggested. The regularized vertices…

In quantum Regge calculus areas of timelike triangles possess discrete spectrum. This is because bivectors of these triangles are variables canonically conjugate to orthogonal connection matrices varying in the compact group. (The scale of…

A path integral measure for gravity should also preserve the fundamental symmetry of general relativity, which is diffeomorphism symmetry. In previous work, we argued that a successful implementation of this symmetry into discrete quantum…

We review some recent attempts to extract information about the nature of quantum gravity, with and without matter, by quantum field theoretical methods. More specifically, we work within a covariant lattice approach where the individual…

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…

We propose a new discrete approximation to the Einstein equations, based on the Capovilla-Dell-Jacobson form of the action for the Ashtekar variables. This formulation is analogous to the Regge calculus in that the curvature has support on…

This paper generalizes our previous paper on the discrete Schwarzschild type solution in the Regge calculus, the simplicial electrodynamics earlier considered in the literature is incorporated in the case of the presence of a charge.…

We investigate quantum gravity in four dimensions using the Regge approach on triangulations of the four-torus with general, non-regular incidence matrices. We find that the simplicial lattice tends to develop spikes for vertices with low…

We develop a model of spatially flat, homogeneous and isotropic cosmology in Lorentzian Regge calculus, employing 4-dimensional Lorentzian frusta as building blocks. By examining the causal structure of the discrete spacetimes obtained by…

We apply the consistent discretization scheme to general relativity particularized to the Gowdy space-times. This is the first time the framework has been applied in detail in a non-linear generally-covariant gravitational situation with…

We review a recent proposal for the construction of a quantum theory of the gravitational field. The proposal is based on approximating the continuum theory by a discrete theory that has several attractive properties, among them, the fact…

Recently, there were works claiming that path integral quantisation of gauge theories necessarily requires relaxation of Lagrangian constraints. As has also been noted in the literature, it is of course wrong since there perfectly exist…

We revise the problem of the quantization of relativistic particle, presenting a modified consistent canonical scheme, which allows one not only to include arbitrary backgrounds in the consideration but to get in course of the quantization…

We present an approach to the canonical quantization of systems with equations of motion that are historically called non-Lagrangian equations. Our viewpoint of this problem is the following: despite the fact that a set of differential…

The arguments were given in a number of our papers that the discrete quantum gravity based on the Regge calculus possesses nonzero vacuum expectation values of the triangulation lengths of the order of Plank scale $10^{-33}cm$. These…