相关论文: Of Connections and Fields
Topological properties play an increasingly important role in future research and technology. This also applies to the field of topological magnetic excitations which has recently become a very active and broad field. In this Perspective…
Three dimensional SU(2) Chern-Simons theory has been studied as a topological field theory to provide a field theoretic description of knots and links in three dimensions. A systematic method has been developed to obtain the link-invariants…
In many areas of applied geometric/numeric computational mathematics, including geo-mapping, computer vision, computer graphics, finite element analysis, medical imaging, geometric design, and solid modeling, one has to compute incidences,…
In this survey article, we present two applications of surface curvatures in theoretical physics. The first application arises from biophysics in the study of the shape of cell vesicles involving the minimization of a mean curvature type…
In this note we present a brief overview of connections between Chern-Simons theory and topological strings. A prominent role in this link has been played by large N dualities and holography. We demystify this by explaining why the Kahler…
Various phenomena related to geometric phases in quantum mechanics are reviewed and explained by analyzing some examples.The concepts of 'parallelism' ,'connections' and 'curvatures' are applied to Aharonov-Bohm (AB) effect, to U(1)phase…
The connection between topology and quantum mechanics is one of the cornerstones of modern physics. Several examples of current interest like the Aharonov-Bohm effect in quantum mechanics, monopoles and instantons in quantum field theory,…
A brief introduction to topological phases is provided, considering several two-band Hamiltonians in one- and two-dimensions. Relevant concepts of the topological insulator theory, such as: Berry phase, Chern number, and the quantum…
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…
There were many attempts to geometrize electromagnetic field and find out new interpretation for quantum mechanics formalism. The distinctive feature of this work is that it combines geometrization of electromagnetic field and…
We study some basic properties and examples of Hermitian metrics on complex manifolds whose traces of the curvature of the Chern connection are proportional to the metric itself.
We give an up-to-date overview of geometric and topological properties of cosymplectic and coKaehler manifolds. We also mention some of their applications to time-dependent mechanics.
The relationship between mathematics and physics has long been an area of interest and speculation. Subscribing to the recent definition by Tegmark, we present a mathematical structure involving the only division rings - the real,…
Using techniques from geometry and complex analysis in their simplest form, we present a derivation of electric fields on surfaces with non-trivial topology. A byproduct of this analysis is an intuitive visualization of elliptic functions…
We provide a formal introduction into the classic theorems of general topology and its axiomatic foundations in set theory. In this second part we introduce the fundamental concepts of topological spaces, convergence, and continuity, as…
These theories, which are surely some of the simplest possible quantum field theories, were introduced in a paper of Dijkgraaf and Witten. The path integral reduces to a finite sum, so it is quite amenable to direct mathematical study.…
Understanding the geometry and topology of configuration or conformational spaces of molecules has relevant applications in chemistry and biology such as the proteins folding problem, drug design and the structure activity relationship…
In this paper we discuss the principles of measuring topological charge or representation traveling in the set of anyons. We describe the procedure and analyze how it works for the different values of parameters of the theory. We also show…
In the geometric theory of defects, media with a spin structure, for example, ferromagnet, is considered as a manifold with given Riemann--Cartan geometry. We consider the case with the Euclidean metric corresponding to the absence of…
In order to account for the observable Universe, any comprehensive theory or model of cosmology must draw from many disciplines of physics, including gauge theories of strong and weak interactions, the hydrodynamics and microphysics of…