Related papers: Foliation, jet bundle and quantization of Einstein…
The equivalence class of absolute configurations of a system under the group of similarity transformations $Sim(3)$ is called the shape of the system. The $Sim(3)$ invariant Lagrangian of the modified Newtonian theory ensures the existence…
The projectability of Poincar\'e-Cartan forms in a third-order jet bundle $J^3\pi$ onto a lower-order jet bundle is a consequence of the degenerate character of the corresponding Lagrangian. This fact is analyzed using the constraint…
For scalar field theories, such as those EFTs describing the Higgs, it is well-known that the 2-derivative Lagrangian is captured by geometry. That is, the set of operators with exactly 2 derivatives can be obtained by pulling back a metric…
General aspects of vielbein representation, ADM formulation and canonical quantization of gravity are reviewed using pure gravity in three dimensions as a toy model. The classical part focusses on the role of observers in general…
We study embedding gravity, a modified theory of gravity, in which our space-time is assumed to be a four-dimensional surface in flat ten-dimensional space. Based on a simple geometric idea, this theory can be reformulated as General…
We consider a discrete model of euclidean quantum gravity in four dimensions based on a summation over random simplicial manifolds. The action used is the Einstein-Hilbert action plus an $R^2$-term. The phase diagram as a function of the…
Dimensional reduction in two dimensions of gravity in higher dimension, or more generally of d=3 gravity coupled to a sigma-model on a symmetric space, is known to possess an infinite number of symmetries. We show that such a bidimensional…
We show how Feynman amplitudes of standard QFT on flat and homogeneous space can naturally be recast as the evaluation of observables for a specific spin foam model, which provides dynamics for the background geometry. We identify the…
We study the approach in which independent variables describing gravity are functions of the space-time embedding into a flat space of higher dimension. We formulate a canonical formalism for such a theory in a form, which requires imposing…
In this paper we present original variational formulations of Yang-Mills, Einstein's gravitation and Kaluza-Klein theories, where, in the spirit of General Relativity, the principal bundle structure over the space-time is not fixed a priori…
In this paper, a careful treatment of extraction of the Hilbert space and constraints from the formal functional integral with the Einstein-Hilbert action is given. The diffeomorphism inavariant measure is worked out using the metric of…
We examine the ADM reformulation of the 5-D KK model: the dimensional reduction is provided to commute with the ADM splitting and we show how the time component of the gauge vector is given by combination of the Lagrangian multipliers for…
Working directly with a general Hamiltonian for the spacetime metric with the $3+1$ decomposition and keeping only the spatial covariance, we investigate the possibility of reducing the number of degrees of freedom by introducing an…
We revisit the holographic renormalization group (RG) setting in which a 4-dimensional ($4d$) quantum field theory at a finite cutoff corresponds to/is described by the Einstein gravity on a part of AdS$_{5}$ space, cutoff at a finite…
Quantum Jet Theory (QJT) is a deformation of QFT where also the quantum dynamics of the observer is taken into account. This is achieved by introducing relative fields, labelled by locations measured by rods relative to the observer's…
We study the dynamics of a modified-gravity theory, which is supplemented by an extended Gibbons-Hawking-York boundary term and incorporates diffeomorphism violation through nondynamical background fields denoted as $u$ and $s^{\mu\nu}$ in…
We discuss black hole quantization in the Wheeler-DeWitt approach. Our consideration is based on a detailed investigation of the canonical formulation of gravity with special considerations of surface terms. Since the phase space of gravity…
Given an autonomous second-order ordinary differential equation (ODE), we define a Riemannian metric on an open subset of the first-order jet bundle. A relationship is established between the solutions of the ODE and the geodesic curves…
We explore the possibility of realizing a non-singular bounce in the early universe within the framework of modified gravity with spacetime torsion. In Einstein Cartan theory, torsion is embedded in the spacetime by adding an antisymmetric…
We quantized the full Einstein equations in a globally hyperbolic spacetime $N=N^{n+1}$, $n\ge 3$, and found solutions of the resulting hyperbolic equation in a fiber bundle $E$ which can be expressed as a product of spatial eigenfunctions…