Related papers: A Primer on Geometric Mechanics
In this Master of Science Thesis I introduce geometric algebra both from the traditional geometric setting of vector spaces, and also from a more combinatorial view which simplifies common relations and operations. This view enables us to…
Visual insights into a wide variety of statistical methods, for both didactic and data analytic purposes, can often be achieved through geometric diagrams and geometrically based statistical graphs. This paper extols and illustrates the…
One considers geometry with the intransitive equaivalence relation. Such a geometry is a physical geometry, i.e. it is described completely by the world function, which is a half of the squared distance function. The physical geometry…
The concept of torsion in geometry, although known for a long time, has not gained considerable attention by the physics community until relatively recently, due to its diverse and potentially important applications to a plethora of…
This is a short introduction to affine and convex spaces, written especially for physics students. It summarizes different elementary presentations available in the mathematical literature, and blends analytic- and geometric-flavoured…
This is the first chapter of an introductory text under construction; further chapters are available via the authors' web pages. Our aim is to provide an elementary access to Cox rings and their applications in algebraic and arithmetic…
A high-school exercise is used to get an insight into planetary motion.
The present text is a collection of notes about differential geometry prepared to some extent as part of tutorials about topics and applications related to tensor calculus. They can be regarded as continuation to the previous notes on…
The setting of metric spaces is very natural for numerous questions concerning manifolds, norms, and fractal sets, and a few of the main ingredients are surveyed here.
This is a guided tour through some selected topics in geometric analysis. We have chosen to illustrate many of the basic ideas as they apply to the theory of minimal surfaces. This is, in part, because minimal surfaces is, if not the…
This article explores the overall geometric manner in which human beings make sense of the world around them by means of their physical theories; in particular, in what are nowadays called pregeometric pictures of Nature. In these, the…
The earlier approach is used for description of qubits and geometric phase parameters, the things critical in the area of topological quantum computing. The used tool, Geometric (Clifford) Algebra is the most convenient formalism for that…
We show that, in spite of a rather common opinion, quantum mechanics can be represented as an approximation of classical statistical mechanics. The approximation under consideration is based on the ordinary Taylor expansion of physical…
The geometry of jets of submanifolds is studied, with special interest in the relationship with the calculus of variations. A new intrinsic geometric formulation of the variational problem on jets of submanifolds is given. Working examples…
The logical line is traced of formulation of theory of mechanics founded on the basic correlations of mathematics of hypercomplex numbers and associated geometric images. Namely, it is shown that the physical equations of quantum, classical…
After an historical introduction on the standard algebraic approach to quantum mechanics of large systems we review the basic mathematical aspects of the algebras of unbounded operators. After that we discuss in some details their relevance…
The main topic of this article is a discussion about the best way to show students that the proportionality of mass and weight, strictly true for point-like particles, is an excellent approximation for objects of "normal" size. The usual…
This short note is intended to review the foundations of mechanics, trying to present them with the greatest mathematical and conceptual clarity. It was attempted to remove most of inessential, even parasitic issues, which can hide the true…
A number of topics involving metrics and measures are discussed, including some of the special structure associated with ultrametrics.
We search for a possible mathematical formulation of some of the key ideas of the relational interpretation of quantum mechanics and study their consequences. We also briefly overview some proposals of relational quantum mechanics for an…