相关论文: Topology and physics-a historical essay

A speculative discussion on the role of various symmetries in physics.

The role of global topology in the dynamics of the Universe is poorly understood. Along with observational programmes for determining the topology of the Universe, some small theoretical steps have recently been made. Heuristic…

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.

Time has entered the domain of topological phases in the field of non-Hermitian physics. Previous studies have relied on periodic modulation in time to make an intuitive connection to established spatial topological invariants, albeit with…

After mathematicians and physicists had learned that the structure of physical space was not necessarily Euclidean, it became conceivable that the global topological structure of space was non-trivial. In the context of the late 19th…

Econophysics embodies the recent upsurge of interest by physicists into financial economics, driven by the availability of large amount of data, job shortage in physics and the possibility of applying many-body techniques developed in…

This introductory text arises from a lecture given in G\"oteborg, Sweden, given by the first author and is intended for undergraduate students, as well as for any mathematically inclined reader wishing to explore a synthesis of ideas…

We discuss twisted cohomology, not just for ordinary cohomology but also for $K$-theory and other exceptional cohomology theories, and discuss several of the applications of these in mathematical physics. Our list of applications is by no…

We review the developments of the statistical physics of fracture and earthquake over the last four decades. We argue that major progress has been made in this field and that the key concepts should now become integral part of the (under-)…

Going back to the early days in the history of quantum mechanics, the interaction of quantum and classical systems stands among the most intriguing open questions in science and makes its appearance in several fields, from physics to…

``One could imagine that as a result of enormously extended astronomical experience, the entire universe consists of countless identical copies of our Milky Way, that the infinite space can be partitioned into cubes each containing an…

The chapter provides an introduction to the basic concepts of Algebraic Topology with an emphasis on motivation from applications in the physical sciences. It finishes with a brief review of computational work in algebraic topology,…

In the period from about 1890 to 1915 an interdisciplinary and unifying research programme known as "cosmical physics" attracted much scientific and public attention. It typically included aspects of the earth sciences (such as magnetic…

This is a position paper written as an introduction to the special volume on quantum algorithms I edited for the journal Mathematical Structures in Computer Science (Volume 20 - Special Issue 06 (Quantum Algorithms), 2010).

This is an expository paper on the subject of the title. It assumes basic scheme theory, commutative and homological algebra.

Cosmology and high energy physics are two closely connected areas. In this lecture I present an example of their rich interplay.

Current theories of particle physics lead to the unavoidable conclusion that there must have been several phase transitions in the early universe. Further, in the context of these theories, it is possible that cosmological phase transitions…

Free actions of finite groups on spheres give rise to topological spherical space forms. The existence and classification problems for space forms have a long history in the geometry and topology of manifolds. In this article, we present a…

A paper of Thomas Young (1773-1829) on the behavior of streams of air makes a good starting point for discussing the not always fair, sometimes serendipitous, association of a physical phenomenon with its discoverer. In a didactic context,…

This paper is the fourth in a series whose goal is to develop a fundamentally new way of building theories of physics. The motivation comes from a desire to address certain deep issues that arise in the quantum theory of gravity. Our basic…