Related papers: A brief introduction to quantum groups
In this thesis I present a short review of ideas in quantum information theory. The first chapter contains introductory material, sketching the central ideas of probability and information theory. Quantum mechanics is presented at the level…
The aim of this paper is to provide an overview of the results about classification of quantum groups that were obtained in arXiv:1303.4046 [math.QA] and arXiv:1502.00403 [math.QA].
These lecture notes are an informal introduction to the theory of computational complexity and its links to quantum computing and statistical mechanics.
Quantum Theory is one of the pillars of modern science developed over the last hundred years. In this review paper we introduce, step by step, the quantum theory understood as a mathematical model describing quantum experiments. We start…
This paper is an essentially self-contained and rigorous description of the fundamental principles of quantum computing from a mathematical perspective. It is intended to help mathematicians who want to get a grasp of this quickly growing…
Notes of a 8h course given at the University of G\"oteborg during an Erasmus exchange visit, June 11-15, 2018. It is intended for PhD and graduate students familiar with $C^*$-algebras but not specializing in quantum groups. The proofs, if…
A brief summary of the physics of low-dimensional quantum systems is given. The material should be accessible to advanced physics undergraduate students. References to recent review articles and books are provided when possible.
These notes are an introduction to the theory of quantum symmetries of finite and infinite sets, graphs, and locally compact spaces.
These lecture notes were created for a graduate-level course on quantum simulation taught at Leibniz University Hannover in 2013. The first part of the course discusses various state of the art methods for the numerical description of…
We give an elementary introduction to the theory of algebraic and topological quantum groups (in the spirit of S. L. Woronowicz). In particular, we recall the basic facts from Hopf (*-) algebra theory, theory of compact (matrix) quantum…
These notes grew out of two lectures I have given on CAT(0) cube complexes. I've tried to keep the material elementary and self-contained in order to keep the material easily accessible and to provide an elementary introduction on the topic…
In Part I of this series we presented the general ideas of applying group-algebraic methods for describing quantum systems. The treatment was there very "ascetic" in that only the structure of a locally compact topological group was used.…
We provide a rather extended introduction to the group field theory approach to quantum gravity, and the main ideas behind it. We present in some detail the GFT quantization of 3d Riemannian gravity, and discuss briefly the current status…
For a century, quantum theorists have been reading the mathematical entrails of quantum mechanics (QM) to divine the nature of quantum reality. But to little avail. In this paper a different approach is taken, namely to identify and explain…
This is a short, self-contained expository survey, focused on algebraic and analytic aspects of quantum groups. Topics covered include the definition of ``quantum group,'' the Yang-Baxter equation, quantized universal enveloping algebras,…
The aim of this textbook is to bridge in regard of quantum computation what proves to be a considerable threshold even to the usual science trained readership between the level of science popularization, and on the other hand, the presently…
This introductory text on the basics of quantum mechanics is intended to serve as a kind of travel guide through the quantum world. It starts by asking whether quantum physics is important, or weird, or incomprehensible. It explains why…
This is an introduction to the quantum groups, or rather to the simplest quantum groups. The idea is that the unitary group $U_N$ has a free analogue $U_N^+$, whose standard coordinates $u_{ij}\in C(U_N^+)$ are allowed to be free, and the…
Group Theory has become an invaluable tool in the physics community. Despite numerous introductory books, the subject remains challenging for beginners. Mathematica has emerged as a popular tool for research and education, offering various…
These lectures present some basic facts in field theory necessary to understand the quantum theory of the Standard Model of weak and electromagnetic interactions.