Related papers: Area expectation values in quantum area Regge calc…
Quantum area tensor Regge calculus is considered, some properties are discussed. The path integral quantisation is defined for the usual length-based Regge calculus considered as a particular case (a kind of a state) of the area tensor…
The quantum measure in area tensor Regge calculus can be constructed in such the way that it reduces to the Feynman path integral describing canonical quantisation if the continuous limit along any of the coordinates is taken. This…
Because of unboundedness of the general relativity action, Euclidean version of the path integral in general relativity requires definition. Area tensor Regge calculus is considered in the representation with independent area tensor and…
Regge calculus configuration superspace can be embedded into a more general superspace where the length of any edge is defined ambiguously depending on the 4-tetrahedron containing the edge. Moreover, the latter superspace can be extended…
A comparative analysis of the versions of quantum measure in the area tensor Regge calculus is performed on the simplest configurations of the system. The quantum measure is constructed in such the way that it reduces to the Feynman path…
Euclidean quantum measure in Regge calculus with independent area tensors is considered using example of the Regge manifold of a simple structure. We go over to integrations along certain contours in the hyperplane of complex connection…
Encountered in the literature generalisations of general relativity to independent area variables are considered, the discrete (generalised Regge calculus) and continuum ones. The generalised Regge calculus can be either with purely area…
We propose the following way of constructing quantum measure in Regge calculus: the full discrete Regge manifold is made continuous in some direction by tending corresponding dimensions of simplices to zero, then functional integral measure…
Wick rotation in area tensor Regge calculus is considered. The heuristical expectation is confirmed that the Lorentzian quantum measure on a spacelike area should coincide with the Euclidean measure at the same argument. The consequence is…
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…
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,…
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…
The infinite-time average of the expectation values of local fields of any interacting quantum theory after a global quench process are key quantities for matching theoretical and experimental results. For quantum integrable field theories,…
We introduce a modified Regge calculus for general relativity on a triangulated four dimensional Riemannian manifold where the fundamental variables are areas and a certain class of angles. These variables satisfy constraints which are…
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…
This article begins with a review of quantum measure spaces. Quantum forms and indefinite inner-product spaces are then discussed. The main part of the paper introduces a quantum integral and derives some of its properties. The quantum…
Regge calculus minisuperspace action in the connection representation has the form in which each term is linear over some field variable (scale of area-type variable with sign). We are interested in the result of performing integration over…
Area Regge calculus is a candidate theory of simplicial gravity, based on the Regge action with triangle areas as the dynamical variables. It is characterized by metric discontinuities and vanishing deficit angles. Area Regge calculus…
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…
The construction of a consistent theory of quantum gravity is a problem in theoretical physics that has so far defied all attempts at resolution. One ansatz to try to obtain a non-trivial quantum theory proceeds via a discretization of…