Related papers: Introduction to abelian anyons in planar systems
To the working physicist, anyon theory is meant to describe certain quasi-particle excitations occurring in two dimensional topologically ordered systems. A typical calculation using this theory will involve operations such as $\otimes$ to…
Relativistic and nonrelativistic anyons are described in a unified formalism by means of the coadjoint orbits of the symmetry groups in the free case as well as when there is an interaction with a constant electromagnetic field. To deal…
In this article we present a pedagogical introduction of the main ideas and recent advances in the area of topological quantum computation. We give an overview of the concept of anyons and their exotic statistics, present various models…
The dichotomy between fermions and bosons is at the root of many physical phenomena, from metallic conduction of electricity to super-fluidity, and from the periodic table to coherent propagation of light. The dichotomy originates from the…
We analyze the quantum mechanics of anyons on the sphere in the presence of a constant magnetic field. We introduce an operator method for diagonalizing the Hamiltonian and derive a set of exact anyon energy eigenstates, in partial…
In this set of lectures, we will start with a brief pedagogical introduction to abelian anyons and their properties. This will essentially cover the background material with an introduction to basic concepts in anyon physics, fractional…
A rough overview is given over the most essential structures underlying all working quantum theoretical models as well as axiomatic and algebraic quantum field theory .
Anyon models are algebraic structures that model universal topological properties in topological phases of matter and can be regarded as mathematical characterization of topological order in two spacial dimensions. It is conjectured that…
We give an elementary introduction to the theory of causal fermion systems, with a focus on the underlying physical ideas and the conceptual and mathematical foundations.
Studying quantum entanglement in systems of indistinguishable particles, in particular anyons, poses subtle challenges. Here, we investigate a model of one-dimensional anyons defined by a generalized algebra. This algebra has the special…
The emergence of non-Abelian anyons from large collections of interacting elementary particles is a conceptually beautiful phenomenon with important ramifications for fault-tolerant quantum computing. Over the last few decades the field has…
We give a presentation of abelian class field theory.
In these lectures we present a few topics in Quantum Field Theory in detail. Some of them are conceptual and some more practical. They have been selected because they appear frequently in current applications to Particle Physics and String…
This introductory work combines bottom-up and top-down approaches towards understanding the underlying categorical structure of possible unifying theories descending from string theory. Guided by well-established developments in the realm…
In this set of lectures, we give a pedagogical introduction to the subject of anyons. We discuss 1) basic concepts in anyon physics, 2) quantum mechanics of two anyon systems, 3) statistical mechanics of many anyon systems, 4) mean field…
In the paper we investigate the theory of quantum optical systems. As an application we integrate and describe the quantum optical systems which are generically related to the classical orthogonal polynomials. The family of coherent states…
A model-independent formulation of anyons as spinning particles is presented. The general properties of the classical theory of (2+1)-dimensional relativistic fractional spin particles and some properties of their quantum theory are…
In this letter we present some new results on modular theory and its application in quantum field theory. In doing this we develop some new proposals how to generalize concepts of geometrical action. Therefore the spirit of this letter is…
(2+1)-dimensional relativistic fractional spin particles are considered within the framework of the group-theoretical approach to anyons starting from the level of classical mechanics and concluding by the construction of the minimal set of…
In these notes, we present a rigorous and self-contained introduction to the fundamental concepts and methods of quantum many-body theory. The text is designed to provide a solid theoretical foundation for the study of interacting quantum…