Related papers: A brief introduction to quantum groups
Formulating a quantum theory of gravity lies at the heart of fundamental theoretical physics. This collection of lecture notes encompasses a selection of topics that were covered in six mini-courses at the Nordita PhD school "Towards…
These notes give a short introduction to finite Coxeter groups, their classification, and some parts of their representation theory, with a focus on the infinite families. They are based on lectures delivered by the author at the…
In this paper, we examine the state art of quantum computing and analyze its potential effects in scientific computing and cybersecurity. Additionally, a non-technical description of the mechanics of the listed form of computing is provided…
The term quantum logic has different connotations for different people, having been considered as everything from a metaphysical attack on classical reasoning to an exercise in abstract algebra. Our aim here is to give a uniform…
This document is meant as a pedagogical introduction to the modern language used to talk about quantum theory, especially in the field of quantum information. It assumes that the reader has taken a first traditional course on quantum…
Quantum gravity is the missing piece in our understanding of the fundamental interactions today. Given recent observational breakthroughs in gravity, providing a quantum theory for what lies beyond general relativity is more urgent than…
This article is based on an invited talk given at the Workshop on Mathematical Physics Towards XXIst Century, held at Beer-Sheva, Israel in 1993. It contains an introduction to quantum gravity for mathematical physicists with an emphasis on…
These are the lecture notes for a course that I am teaching at Zhiyuan College of Shanghai Jiao Tong University (available at https://www.youtube.com/derekkorg), though the first draft was created for a previous course I taught at the…
There is compelling theoretical evidence that quantum physics will change the face of information science. Exciting progress has been made during the last two decades towards the building of a large scale quantum computer. A quantum group…
As a result of the capabilities of quantum information, the science of quantum information processing is now a prospering, interdisciplinary field focused on better understanding the possibilities and limitations of the underlying theory,…
This is a survey on old and new results as well as an introduction to various related basic notions and concepts, based on two talks given at the International Workshop on Geometry and Analysis in Kemerovo (Sobolev Institute of Mathematics,…
This is an overview of the basics of inverse semigroup theory written for the Workshop on Semigroups and Categories held at the University of Ottawa in 2010.
The paper is devoted to the mathematical foundation of the quantum tomography using the theory of square-integrable representations of unimodular Lie groups.
The interpretation of quantum mechanics has been discussed since this theme first was brought up by Einstein and Bohr. This article describes a proposal for a new foundation of quantum theory, partly drawing upon ideas from statistical…
Quantum field theory has formed the conceptual framework of most of physics for more than sixty years. It incorporates a complete revision of our conception of the nature of matter and existence itself. Yet it is rarely taught, or even…
The ongoing progress in quantum theory emphasizes the crucial role of the very basic principles of quantum theory. However, this is not properly followed in teaching quantum mechanics on the graduate and undergraduate levels of physics…
There is a unique finite group that lies inside the 2-dimensional unitary group but not in the special unitary group, and maps by the symmetric square to an irreducible subgroup of the 3-dimensional real special orthogonal group. In an…
Phenomenological models of quantum gravity often consider the existence of some form of minimal length. This feature is commonly described in the context of quantum mechanics and using the corresponding formalism and techniques. Although…
This invited chapter in the Handbook of Quantum Logic and Quantum Structures consists of two parts: 1. A substantially updated version of quant-ph/0402130 by the same authors, which initiated the area of categorical quantum mechanics, but…
These notes are from a series of lectures given at the Universidad de Los Andes in Bogot\'a, Colombia on some topics of current interest in quantum information. While they aim to be self-contained, they are necessarily incomplete and…