相关论文: 2-dimensional Regge gravity in the conformal gauge
By regularizing the conical singularities by means of a segment of a sphere or pseudosphere and then taking the regulator to zero, we compute exactly the Faddeev--Popov determinant related to the conformal gauge fixing for a piece-wise flat…
By regularizing the singularities appearing in the two dimensional Regge calculus by means of a segment of a sphere or pseudo-sphere and then taking the regulator to zero, we obtain a simple formula for the gauge volume which appears in the…
We adopt the standard definition of diffeomorphism for Regge gravity in D=2 and give an exact expression of the Liouville action in the discretized case. We also give the exact form of the integration measure for the conformal factor. In…
The functional integral measure in the 4D Regge calculus normalised w.r.t. the DeWitt supermetric on the space of metrics is considered. The Faddeev-Popov factor in the measure is shown according to the previous author's work on the…
The problem of fixing measure in the path integral for the Regge-discretised gravity is considered from the viewpoint of it's "best approximation" to the already known formal continuum general relativity (GR) measure. A rigorous formulation…
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.…
Regge's method for regularizing euclidean quantum gravity is applied to two dimensional gravity. We use two different strategies to simulate the Regge path integral at a fixed value of the total area: A standard Metropolis simulation…
One of several possibilities to construct a quantum theory of gravity is employing the Feynman path integral. This approach is plagued by some problems: the integration measure is not uniquely defined, the Einstein-Hilbert action unbounded,…
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 of our recent work on the conformal geometry corresponding to the triangulated surfaces used in 2-dimensional simplicial quantum gravity. In particular, we discuss the regularized Liouville action associated with random Regge…
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…
Regge's method for regularizing euclidean quantum gravity is applied to two dimensional gravity. Using topologies with genus zero and two and a scale invariant measure, we show that the Regge method fails to reproduce the values of the…
This Ph.D. thesis pursues two goals: The study of the geometrical structure of two-dimensional quantum gravity and in particular its fractal nature. To address these questions we review the continuum formalism of quantum gravity with…
By adopting the standard definition of diffeomorphisms for a Regge surface we give an exact expression of the Liouville action both for the sphere and the torus topology in the discretized case. The results are obtained in a general way by…
We study the Faddeev formulation of gravity in which the metric is composed of vector fields. This system is reducible with the help of the equations of motion to the general relativity. The Faddeev action is evaluated for the piecewise…
It is well known that one can parameterize 2-D Riemannian structures by conformal transformations and diffeomorphisms of fiducial constant curvature geometries; and that this construction has a natural setting in general relativity theory…
Quantum gravity is studied in the path integral formulation applying the Regge calculus. Restricting the quadratic link lengths of the originally triangular lattice the path integral can be transformed to the partition function of a spin…
We consider minisuperspace gravity system described by piecewise flat metric discontinuous on three-dimensional faces (tetrahedra). There are infinite terms in the Einstein action. However, starting from proper regularization, these terms…
A method for consistent quantization of conformal gravity treating conformal symmetry in a very controllable way is presented. First, we discuss local conformal symmetry in the framework of gravitational interactions, where we view it as an…
An approach to the discrete quantum gravity based on the Regge calculus is discussed which was developed in a number of our papers. Regge calculus is general relativity for the subclass of general Riemannian manifolds called piecewise flat…