Related papers: Covariance, Geometricity, Setting, and Dynamical S…
To understand how the human visual system analyzes images, it is essential to know the structure of the visual environment. In particular, natural images display consistent statistical properties that distinguish them from random luminance…
The purpose of this review is to provide a brief overview of some recent conceptual developments about possible criteria to guarantee the uniqueness of the quantization in a variety of situations that are found in cosmological systems.…
Statistical models that possess symmetry arise in diverse settings such as random fields associated to geophysical phenomena, exchangeable processes in Bayesian statistics, and cyclostationary processes in engineering. We formalize the…
The review paper presents generalization of d'Alembert's variational principle: the dynamics of a quantum system for an external observer is defined by the exact equilibrium of all acting in the system forces, including the random quantum…
Quantum mechanics is among the most important and successful mathematical model for describing our physical reality. The traditional formulation of quantum mechanics is linear and algebraic. In contrast classical mechanics is a geometrical…
A complete canonical formulation of general covariance makes it possible to construct new modified theories of gravity that are not of higher-curvature form, as shown here in a spherically symmetric setting. The usual uniqueness theorems…
The field equations of modified gravity theories, when considering a homogeneous and isotropic cosmological model, always become autonomous differential equations. This relies on the fact that in such models all variables only depend on…
Identifying an appropriate set of ``observables'' is a nontrivial task for most approaches to quantum gravity. We describe how it may be accomplished in the context of a recently proposed family of stochastic (but classical) dynamical laws…
This contribution shortly outlines and reviews a theoretical and computational approach for a theory of change concerning systems where it is not possible to apply the laws of motion ab initio. The concept of meta-structure relates to the…
It is believed that a primary principle of the theory of quantum gravity is the Holographic Principle according to which a physical system can be described only by degrees of freedom living on its boundary. The generalized covariant…
The history of general relativity suggests that in absence of experimental data, constructing a theory on philosophical first principles can lead to a very useful theory as well as to ground-breaking insights about physical reality. The two…
In quantum cosmology, one applies quantum physics to the whole universe. While no unique version and no completely well-defined theory is available yet, the framework gives rise to interesting conceptual, mathematical and physical…
This note is to bring to the reader's attention the fact that general relativity and quantum mechanics differ from each other in one main aspect. General relativity is based on the diffeomorphism covariant formulation of the laws of physics…
A fundamental element of scale-dependent gravity is the scale-setting procedure. We present a new covariant expression to set the scale that arises when examining the field equations. Considering the renormalization group equations and…
We examine the general issue of whether a scale dependent cosmological constant can be consistent with general covariance, a problem that arises naturally in the treatment of quantum gravitation where coupling constants generally run as a…
We introduce a geometric formulation of quantum indeterminacy from which the standard uncertainty inequalities emerge as necessary consequences. Our approach is based on convex geometry in phase space and on methods from symplectic…
There is a need in general relativity for a consistent and useful mathematical theory defining the multiplication of tensor distributions in a geometric (diffeomorphism invariant) way. Significant progress has been made through the concept…
General covariance is a crucial notion in the study of field theories in curved spacetime. A field theory defined with respect to a semi-Riemannian metric is generally covariant if two metrics which are related by a diffeomorphism produce…
Classical cosmology exhibits a particular kind of scaling symmetry. The dynamics of the invariants of this symmetry forms a system that exhibits many of the features of open systems such as the non-conservation of mechanical energy and the…
This paper is an extended version of the talk given at 19th Texas Symposium of Relativistic Astrophysics and Cosmology, Paris, 1998. It reviews of some recent work; mathematical details are skipped. It is well-known that a choice of gauge…