相关论文: Topology in Physics - A Perspective
Subject of this article is the relationship between modern cosmology and fundamental physics, in particular general relativity as a theory of gravity on one side, together with its unique application in cosmology, and the formation of…
Basic concepts and definitions in differential geometry and topology which are important in the theory of solitons and instantons are reviewed. Many examples from soliton theory are discussed briefly, in order to highlight the application…
Topological data analysis refers to approaches for systematically and reliably computing abstract ``shapes'' of complex data sets. There are various applications of topological data analysis in life and data sciences, with growing interest…
Why is the manifold topology in a spacetime taken for granted? Why do we prefer to use Riemann open balls as basic-open sets, while there also exists a Lorentz metric? Which topology is a best candidate for a spacetime; a topology…
Despite its amazing quantitative successes and contributions to revolutionary technologies, physics currently faces many unsolved mysteries ranging from the meaning of quantum mechanics to the nature of the dark energy that will determine…
We review the life and remarkable contributions to Physics of Gregor Wentzel.
Hystory of topology is discussed uncluding the Golden Age Period (1950-1970), the Period of Decay (1970-1980) and the Period of Recovery in 80s and 90s based on the ideas borrowed from physics community. In the second part recent result of…
The aim of this paper is to introduce a mathematical logic based approach investigating why-type questions in physics.
The role of mathematical models in physics has for longer been well established. The issue of their proper building and use appears to be less clear. Examples in this regard from relativity and quantum mechanics are mentioned. Comments…
Extended version of an article on top-quark physics, to appear in the May 1997 issue of Physics Today.
This article is a short survey of the history of functional analysis for topologists.
This is an introduction to type theory, synthetic topology, and homotopy type theory from a category-theoretic and topological point of view, written as a chapter for the book "New Spaces for Mathematics and Physics" (ed. Gabriel Catren and…
This is a Concluding Talk, not a Summary of the FPCP 2011 Conference. I will first make some comments on the status and the prospects of particle physics and then review some of the highlights that particularly impressed me at this…
The topological force and torque are investigated in the systems with spin-orbit coupling. Our results show that the topological force and torque appears as a pure relativistic quantum effect in an electromagnetic field. The origin of both…
Recent work by physicists on gravity in two dimensions has a natural generalization to four dimensions, formulated in terms of an analogue of Segal's category [defined for the study of conformal field theory].
Time is, figuratively and literally, becoming the new dimension for crystalline matter. As such, rapid recent progress on time-varying media gave rise to the notion of temporal and spatiotemporal crystals. Fundamentally rethinking the role…
Understanding degrees of freedom in classical mechanics is fundamental to characterizing physical systems. Counting them is usually easy, especially if we can assign them a clear meaning. However, the precise definition of a degree of…
Short survey to be published at the Encyclopedia of Mathematical Physics.
Along with weaving together observations, experiments, and theoretical constructs into a coherent mesh of understanding of the world around us, physics over its past five centuries has continuously refined the base concepts on which the…
The goal of this article is to survey recent developments in the theory of contact structures in dimension three.