Related papers: Path integral measure in Regge calculus from the f…
Gravity-induced quantum interference is a remarkable effect that has already been confirmed experimentally, and it is a phenomenon in which quantum mechanics and gravity play simultaneously an important role. Additionally, a generalized…
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…
We present some aspects of the theory of finite element exterior calculus as applied to partial differential equations on manifolds, especially manifolds endowed with an approximate metric called a Regge metric. Our treatment is intrinsic,…
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…
The transformation of the path integral measure under the reduction procedure in the dynamical systems with a symmetry is considered. The investigation is carried out in the case of the Wiener--type path integrals that are used for…
A new method for nonperturbative investigations of quantum gravity is presented in which the simplicial path integral is approximated by the partition function of a spin system. This facilitates analytical and numerical computations…
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 present a way for calculating the Lagrangian path integral measure directly from the Hamiltonian Schwinger--Dyson equations. The method agrees with the usual way of deriving the measure, however it may be applied to all theories, even…
A new path integral approach of quantum gravity based on relational variables and quantum test objects is presented. We take as a basic variables the squared invariant distance. This invariant quantity is technically simpler to work with…
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 propose a version of the 2D Regge calculus, in which the areas of all triangles are equal to each other. In this discretization Lund - Regge measure over link lengths is simplified considerably. Contrary to the usual Regge models with…
This paper gives a rigorous interpretation of a Feynman path integral on a Riemannian manifold M with non-positive sectional curvature. A $L^2$ Riemannian metric $G_P$ is given on the space of piecewise geodesic paths $H_P(M)$ adapted to…
We revisit the gravity path integral formalism of JT gravity. We explain how to gauge fix the path integral in the presence of asymptotic boundaries and conical defects, and resolve an ambiguity regarding the dilaton gravity operator that…
In Regge calculus the space-time manifold is approximated by certain abstract simplicial complex, called a pseudo-manifold, and the metric is approximated by an assignment of a length to each 1-simplex. In this paper for each pseudomanifold…
We introduce variants of Regge finite element metrics with enhanced properties of the trace. In particular the trace operator is surjective to a finite element space of continuous functions. Multiplying these scalar functions by the…
The analytic structure of the Regge action on a cone in $d$ dimensions over a boundary of arbitrary topology is determined in simplicial minisuperspace. The minisuperspace is defined by the assignment of a single internal edge length to all…
This is an informal review of the formulation of canonical general relativity and of its implications for quantum gravity; the various versions are compared, both in the continuum and in a discretized approximation suggested by Regge…
We describe a theory of quantum gravity which is based on the assumption that the spacetime structure at small distances is given by a piecewise linear (PL) 4-manifold corresponding to a triangulation of a smooth 4-manifold. The fundamental…
Certain natural geometric approximation schemes are developed for Wiener measure on a compact Riemannian manifold. These approximations closely mimic the informal path integral formulas used in the physics literature for representing the…
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.…