Related papers: Geometry and Physics: An Overview
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 ``geometry'', in the sense of the classical differential geometry of smooth manifolds (CDG), is put under scrutiny from the point of view of Abstract Differential Geometry (ADG), along with resulting, thereby, potential physical…
On the occasion of the 100th anniversary of the birth of the quantum idea, the development, achievements, and promises of quantum mechanics are described.
Some conjectures and open problems in convex geometry are presented, and their physical origin, meaning, and importance, for quantum theory and generic statistical theories, are briefly discussed.
Our conventional understanding of space-time, as well as our notion of geometry, break down once we attempt to describe the very early stages of the evolution of our universe. The extreme physical conditions near the Big Bang necessitate an…
Geometrization of physical theories have always played an important role in their analysis and development. In this contribution we discuss various aspects concerning the geometrization of physical theories: from classical mechanics to…
A speculative discussion on the role of various symmetries in physics.
We review, in a historical perspective, developments in physics which led to the emergence of unifying ideas and theories. Some attention is paid to the theoretical programme that started in the second decade of the XXth century and whose…
This is an overview of merging the techniques of Riesz space theory and convex geometry.
The article is an historical overview of some of the major contributions from different areas of Science with which, for centuries, it has been built up a scientific, sound and consistent vision of the atom. Some experiments that led us to…
This century has seen a dramatic increase in observational possibilities of the physics of the universe. Several of the very recent new developments with emphasis on the particle physics aspect and in particular Gamma-Gamma interactions are…
Soft interfaces can mediate interactions between particles bound to them. The force transmitted through the surface geometry on a particle may be expressed as a closed line integral of the surface stress tensor around that particle. This…
In this paper we survey several intersection and non-intersection phenomena appearing in the realm of symplectic topology. We discuss their implications and finally outline some new relations of the subject to algebraic geometry.
Cosmoparticle physics is the natural result of development of mutual relationship between cosmology and particle physics. Its prospects offer the way to study the theory of everything and the true history of the Universe, based on it, in…
This paper traces the seminal roles that physicists and mathematicians have played in the conceptual development of the biological sciences in the past, and especially in the 19th and 20th centuries.
In this survey article, we present interactions between algebraic geometry and computer vision, which have recently come under the header of algebraic vision. The subject has given new insights in multiple view geometry and its application…
The purpose of this essay is to trace the historical development of geometry while focusing on how we acquired mathematical tools for describing the "shape of the universe." More specifically, our aim is to consider, without a claim to…
This short essay traces the conceptual history of micro- and macroscopicity in the context of physical science. By focusing on three distinct episodes spanning five centuries, we show the scientific and philosophical meanings of this…
The differential geometric aspects of Geometric Phases are reviewed.
These notes are an expanded version of an introductory lecture on contact geometry given at the 2001 Georgia Topology Conference. They are intended to present some of the "topological" aspects of three dimensional contact geometry.