Related papers: Conformal decomposition in canonical general relat…

Using the methods of symplectic geometry, we establish the existence of a canonical transformation from potential model Hamiltonians of standard form in a Euclidean space to an equivalent geometrical form on a manifold, where the…

Whereas the nature of dark components in the Universe remains unknown, alternative models of gravity have been developed to offer a geometric explanation to the origin of such components. In this work we use the Minimal Geometric…

We give new solutions of the quantum conformal deformations of the full Maxwell equations in terms of deformations of the plane wave. We study the compatibility of these solutions with the conservation of the current. We also start the…

A modern re-visitation of the consequences of the lack of an intrinsic notion of instantaneous 3-space in relativistic theories leads to a reformulation of their kinematical basis emphasizing the role of non-inertial frames centered on an…

Conformal geometry is considered within a general relativistic framework. An invariant distant for proper time is defined and a parallel displacement is applied in the distorted space-time, modifying Einstein's equation appropriately. A…

Quantum canonical transformations are used to derive the integral representations and Kummer solutions of the confluent hypergeometric and hypergeometric equations. Integral representations of the solutions of the non-periodic three body…

In this paper we consider conformal symmetry in the context of manifolds with general affine connection. We extend the conformal transformation law of the metric to a general metric compatible affine connection, and find that it is a…

A deformation of special relativistic kinematics (possible signal of a theory of quantum gravity at low energies) leads to a modification of the notion of spacetime. At the classical level, this modification is required when one considers a…

In the present paper we give conclusive arguments pointing at physical equivalence among conformally related metrics. Based on the argument that any consistent effective theory of spacetime must be invariant under the one-parameter group of…

We first find the linear approximation of the second plus fourth order derivative massive conformal gravity action. Then we reduce the linearized action to separated second order derivative terms, which allows us to quantize the theory by…

Based on the de Broglie-Bohm relativistic quantum theory of motion we show that the conformal formulation of general relativity, being linked with a Weyl-integrable geometry, may implicitly contain the quantum effects of matter. In this…

We study the introduction of holonomy corrections in $f(R)$ gravity. We will show that there are infinitely many ways, as many as canonical transformations, to introduce this kind of corrections, depending on the canonical variables (two…

Degenerate geometrical configurations in quantum gravity are important to understand if the fate of classical singularities is to be revealed. However, not all degenerate configurations arise on an equal footing, and one must take into…

Loop quantum cosmology in (b, v) variables, which is governed by a unit step size difference equation, is embedded into a full theory context based on similar variables. A full theory context here means a theory of quantum gravity arrived…

This paper is the first of two papers devoted to formulation of quantum mechanics of a particle in a normal geodesic frame of reference in the general Riemannian space-time. Here canonical quantization of geodesic motion in the…

We use a canonical parametrization of twisted geometries describing the classical phase space of loop quantum gravity on a fixed graph, and establish its explicit correspondence with the associated frame bases and spinorial descriptions.…

We prove that semiclassical gravity in conformally static, globally hyperbolic spacetimes with a massless, conformally coupled Klein-Gordon field is well posed, when viewed as a coupled theory for the dynamical conformal factor of the…

The groupoid approach to noncommutative unification of general relativity with quantum mechanics is compared with the canonical gravity quantization. It is shown that by restricting the corresponding noncommutative algebra to its…

Loop quantum gravity is a mature theory. To proceed to explicit calculations in cosmology, it is necessary to make assumptions and simplifications based on the symmetries of the cosmological setting. Symmetry reduction is especially…

A general classical theorem is presented according to which all invariant relations among the space time metric scalars, when turned into functions on the Phase Space of full Pure Gravity (using the Canonical Equations of motion), become…