相关论文: Of Connections and Fields

The object of this contribution is twofold. On one hand, it rises some general questions concerning the definition of the electromagnetic field and its intrinsic properties, and it proposes concepts and ways to answer them. On the other…

Reducing a 3-dimensional Chern-Simons term by a symmetry yields other topologically interesting structures. Specifically, reducing by radial symmetry results in a 1-dimensional quantum mechanical model, which has recently been used in an…

In Part 1 of this study we showed, for a wide range of geometries, that the relationships between their concept-sets are fully determined by those between their (affine) automorphism groups. In this (self-contained) part, we show how this…

There are two natural Chern-Simons theories associated with the embedding of a three-dimensional surface in Euclidean space; one is constructed using the induced metric connection -- it involves only the intrinsic geometry, the other is…

We study the quantum mechanics of a system of topologically interacting particles in 2+1 dimensions, which is described by coupling the particles to a Chern-Simons gauge field of an inhomogeneous group. Analysis of the phase space shows…

Within a relativistic quantum formalism we examine the role of second-order corrections caused by the application of magnetic fields in two-dimensional topological and Chern insulators. This allows to reach analytical expressions for the…

In this article, the notion of a mathematical model in science is attempted to be enlightened from several points of view. In particular, it is shown that mathematical models are introduced differently and used differently in different…

Motivated by the observation of the fractional quantum Hall effect in graphene, we consider the effective field theory of relativistic quantum Hall states. We find that, beside the Chern-Simons term, the effective action also contains a…

Quantum metrology is deeply connected to quantum geometry, through the fundamental notion of quantum Fisher information. Inspired by advances in topological matter, it was recently suggested that the Berry curvature and Chern numbers of…

Some intensive observables of the electronic ground state in condensed matter have a geometrical or even topological nature. In this Review I present the geometrical observables whose expression is known in a full many-body framework,…

We introduce the theoretical framework we use to study the bewildering variety of phases in condensed--matter physics. We emphasize the importance of the breaking of symmetries, and develop the idea of an order parameter through several…

This thesis explores the correspondence between Chern-Simons theory and integrable field theories across different dimensions. It brings together all of my work in this area, including several distinct realizations of this correspondence.…

These lecture notes (from the Second Autumn School in High Energy Physics and Quantum Field Theory, Yerevan 2014) cover a number of topics related to geometric quantization. Most of the material is presented from a physicist's point of…

With the perspective of looking for experimentally detectable physical applications of the so-called topological embedding, a procedure recently proposed by the author for quantizing a field theory around a non-discrete space of classical…

Geometrical model for quantum objects is suggested. It is shown that equations for free material Dirac field and for Maxwell electromagnetic field can be considered as relations describing propagation of the space topological defects. This…

A core level of basic information for physics is identified, based on an analysis of the characteristics of the parameters space, time, mass and charge. At this level, it is found that certain symmetries operate, which can be used to…

This paper is mostly a collection of ideas already published by various authors, some of them even a long time ago. Its intention is to bring the reader to know some rather unknown papers of different fields that merit interest and to show…

Quantum graphs have become in this century a favorite playground for mathematicians, mathematical physicists, and chemists, due to their manifold applications as models of thin structures, as well as presenting sometimes simpler playground…

This article is meant as a gentle introduction to the "topological terms" that often play a decisive role in effective theories describing topological quantum effects in condensed matter systems. We first take up several prominent examples,…

We give a brief review of the application of some topological solutions in field theory.