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We describe recent attempts at discretizing canonical quantum gravity in four dimensions in terms of a connection formulation. This includes a general introduction, a comparison between the real and complex connection approach, and a…
The discovery of cosmic acceleration has raised the intriguing possibility that we are witnessing the first breakdown of General Relativity on cosmological scales. In this article I will briefly review current attempts to construct a…
We describe a completely general and fully non-perturbative framework for constructing dynamical reference frames in generally covariant theories, and for understanding the gauge-invariant observables that they yield. Our approach makes use…
In order to account for the observable Universe, any comprehensive theory or model of cosmology must draw from many disciplines of physics, including gauge theories of strong and weak interactions, the hydrodynamics and microphysics of…
We present a way to apply quantum logic to the study of quantum programs. This is made possible by using an extension of the usual propositional language in order to make transformations performed on the system appear explicitly. This way,…
We apply the conformal gravity theory to a sample of 111 spiral galaxies whose rotation curve data points extend well beyond the optical disk. With no free parameters other than galactic mass to light ratios, the theory is able to account…
Quantum computations operate in the quantum world. For their results to be useful in any way, there is an intrinsic necessity of cooperation and communication controlled by the classical world. As a consequence, full formal descriptions of…
In the current debate referring to the construction of a tenable background independent theory of Quantum Gravity we introduce the notion of topos-theoretic relativization of physical representability and demonstrate its relevance…
We investigate some basic applications of Fractional Calculus (FC) to Newtonian mechanics. After a brief review of FC, we consider a possible generalization of Newton's second law of motion and apply it to the case of a body subject to a…
We discuss an approach to gravitational waves based on Geometric Algebra and Gauge Theory Gravity. After a brief introduction to Geometric Algebra (GA), we consider Gauge Theory Gravity, which uses symmetries expressed within the GA of flat…
This overview paper reviews several results relating the representation theory of quivers to algebraic geometry and quantum group theory. (Potential) applications to the study of the representation theory of wild quivers are discussed. To…
D-branes are by now an integral part of our toolbox towards understanding nature. In this review we will describe recent progress in their use to realize fundamental interactions. The realization of the Standard Model and relevant physics…
Possibility of gravitational repulsion in General Relativity is discussed and astronomical data in favor of cosmological acceleration are described. The problem of vacuum energy is emphasized and possible ways of its solution are indicated.…
Starting from a description of various generalized function algebras based on sequence spaces, we develop the general framework for considering linear problems with singular coefficients or non linear problems. Therefore, we prove…
This article is meant as a summary and introduction to the ideas of effective field theory as applied to gravitational systems. Contents: 1. Introduction 2. Effective Field Theories 3. Low-Energy Quantum Gravity 4. Explicit Quantum…
Alternative theories of gravity have been recently studied in connection with their cosmological applications, both in the Palatini and in the metric formalism. The aim of this paper is to propose a theoretical framework (in the Palatini…
IAU 2000 resolutions on the reference frames set up a solid theoretical foundation for implementing general relativity in astronomical data processing algorithms and for unambiguous interpretation of measured relativistic effects. We…
These are lecture notes on the algebraic approach to regular languages. The classical algebraic approach is for finite words; it uses semigroups instead of automata. However, the algebraic approach can be extended to structures beyond…
Some ideas about phenomenological applications of quantum algebras to physics are reviewed. We examine in particular some applications of the algebras $U_ q (su_2)$ and $U_{qp}({\rm u}_2)$ to various dynamical systems and to atomic and…
Numerical simulations are becoming a more effective tool for conducting detailed investigations into the evolution of our universe. In this article, we show how the framework of numerical relativity can be used for studying cosmological…