Cartan approach to Teleparallel Equivalent to General Relativity: A review

In previous works, questioning the mathematical nature of the connection in the translations gauge theory formulation of Teleparallel Equivalent to General Relativity (TEGR) Theory led us to propose a new formulation using a Cartan connection. In this review, we summarize the presentation of that proposal and discuss it from a gauge theoretic perspective.

On a new field theory formulation and a space-time adjustment that predict the same precession of Mercury and the same bending of light as general relativity

This article introduces a new field theory formulation. The new field theory formulation recognizes vector continuity as a general principle and begins with a field that satisfies vector continuity equations. Next, independent of the new formulation, this article introduces a new space-time adjustment. Then, we solve the one-body gravitational problem by applying the space-time adjustment to the new field theory formulation. With the space-time adjustment, the new formulation predicts precisely the same precession of Mercury and the same bending of light as general relativity. The reader will find the validating calculations to be simple. The equations of motion that govern the orbital equations are in terms of Cartesian coordinates and time. An undergraduate college student, with direction, can perform the validations.

Data driven theory for knowledge discovery in the exact sciences with applications to thermonuclear fusion

In recent years, the techniques of the exact sciences have been applied to the analysis of increasingly complex and non-linear systems. The related uncertainties and the large amounts of data available have progressively shown the limits of the traditional hypothesis driven methods, based on first principle theories. Therefore, a new approach of data driven theory formulation has been developed. It is based on the manipulation of symbols with genetic computing and it is meant to complement traditional procedures, by exploring large datasets to find the most suitable mathematical models to interpret them. The paper reports on the vast amounts of numerical tests that have shown the potential of the new techniques to provide very useful insights in various studies, ranging from the formulation of scaling laws to the original identification of the most appropriate dimensionless variables to investigate a given system. The application to some of the most complex experiments in physics, in particular thermonuclear plasmas, has proved the capability of the methodology to address real problems, even highly nonlinear and practically important ones such as catastrophic instabilities. The proposed tools are therefore being increasingly used in various fields of science and they constitute a very good set of techniques to bridge the gap between experiments, traditional data analysis and theory formulation.