Related papers: Barbero-Immirzi parameter in Regge calculus
Let $d\gamma(x)\equiv\pi^{-n/2}e^{-|x|^2}dx$ for all $x\in{\mathbb R}^n$ be the Gauss measure on ${\mathbb R}^n$. In this paper, the authors establish the characterizations of the space BMO$(\gamma)$ of Mauceri and Meda via commutators of…
Given closed Riemannian manifold $(M^n, g)$ of positive Ricci curvature $Ricci(g) \geq (n-1)g$ we study isoperimetric regions on the spherical cone over $M$. When $g$ is Einstein we use this to compute the Yamabe constant of $(M \times {\bf…
Space-time measurements, of gedanken experiments of special relativity need modification in curved spaces-times. It is found that in a space-time with metric $g$, the special relativistic factor $\gamma$, has to be replaced by…
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…
In this paper the quantum cosmological consequences of introducing a term cubic in the Ricci curvature scalar $R$ into the Einstein--Hilbert action are investigated. It is argued that this term represents a more generic perturbation to the…
In a consistent heterotic string theory, the Kalb-Ramond field, which is the source of spacetime torsion, is augmented by Yang-Mills and gravitational Chern-Simons terms. When compactified to 4-dimensions and in the field theory limit, such…
We consider the possibility to use the areas of two-simplexes, instead of lengths of edges, as the dynamical variables of Regge calculus. We show that if the action of Regge calculus is varied with respect to the areas of two-simplexes, and…
Based on the first-order action for scalar-tensor theories with the Immirzi parameter, the symplectic form for the spacetimes admitting a weakly isolated horizon as internal boundary is derived by the covariant phase space approach. The…
A Lorentz and gauge symmetry preserving regularization method is discussed in four dimension based on momentum cutoff. We use the conditions of gauge invariance or equivalently the freedom of shift of the loop momentum to define the…
The formula for the area eigenvalues that was obtained by many authors within the approach known as loop quantum gravity states that each edge of a spin network contributes an area proportional to sqrt{j(j+1)} times Planck length squared to…
One of the qualitatively distinct and robust implication of Loop Quantum Gravity (LQG) is the underlying discrete structure. In the cosmological context elucidated by Loop Quantum Cosmology (LQC), this is manifested by the Hamiltonian…
The canonical structure of the Einstein-Hilbert Lagrange density $L=\sqrt{-g}R$ is examined in two spacetime dimensions, using the metric density $h^{\mu \nu}\equiv \sqrt{-g}g^{\mu \nu}$ and symmetric affine connection $\Gamma_{\sigma…
The relation between Loop Quantum Gravity and Regge calculus has been pointed out many times in the literature. In particular the large spin asymptotics of the Barrett-Crane vertex amplitude is known to be related to the Regge action. In…
We study and compare the spectra of geometric operators (length and area) in the quantum kinematics of two formulations of three-dimensional Lorentzian loop quantum gravity. In the SU(2) Ashtekar-Barbero framework, the spectra are discrete…
In this work, we have discussed a spatially homogeneous and anisotropic Bianchi type-I space-time in the presence of Barrow holographic dark energy (infrared cut-off is the Hubble's horizon) proposed by Barrow recently (Physics Letters B…
{\it In Bargmann representation, the reggeon's field theory{\color{blue} [5]} is caracterized by the non symmetrical Gribov operator $\displaystyle{H_{\lambda',\mu,\lambda} = \lambda' A^{*^{2}}A^{2} + \mu A^{*}A + i\lambda A^{*}(A +…
The quantum-mechanical framework in which observables are associated with Hermitian operators is too narrow to discuss measurements of such important physical quantities as elapsed time or harmonic-oscillator phase. We introduce a broader…
A systematic Hamiltonian formulation of the Einstein-Cartan system, based on the Hilbert-Palatini action with the Barbero-Immirzi and cosmological constants, is performed using the traditional ADM decomposition and without fixing the time…
The configuration space of the reduced Hamiltonian formulation of quantum gravity has been shown, for non-Ricci flat metrics, to be a higher-dimensional analogue of the Teichm\"{u}ller space of conformal structures on a Riemann surface. In…
In this paper we suggest gauge invariant discretization of Poincare quantum gravity. We generalize Regge calculus to the case of Riemann-Cartan space. The basic element of the constructed discretization is piecewize linear Riemann-Cartan…