Related papers: An Introduction to Quantum Algebras and Their Appl…
The idea that the Universe is a program in a giant quantum computer is both fascinating and suffers from various problems. Nonetheless, it can provide a unified picture of physics and this can be very useful for the problem of Quantum…
Geometrization of physical theories have always played an important role in their analysis and development. In this contribution we discuss various aspects concerning the geometrization of physical theories: from classical mechanics to…
Quantum computation is a rapidly progressing field today. What are its principles? In what sense is it distinct from conventional computation? What are its advantages and disadvantages? What type of problems can it address? How practical is…
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 is an introduction to quantum gravity, aimed at a fairly general audience and concentrating on what have historically two main approaches to quantum gravity: the covariant and canonical programs (string theory is not covered). The…
The purpose of this paper is to make the theory of vertex algebras trivial. We do this by setting up some categorical machinery so that vertex algebras are just ``singular commutative rings'' in a certain category. This makes it easy to…
Algebraic quantum field theory is an approach to relativistic quantum physics, notably the theory of elementary particles, which complements other modern developments in this field. It is particularly powerful for structural analysis but…
Quantum mechanics is among the most important and successful mathematical model for describing our physical reality. The traditional formulation of quantum mechanics is linear and algebraic. In contrast classical mechanics is a geometrical…
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.
We describe a connection between finite--dimensional representations of quantum affine algebras and affine Hecke algebras.
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…
Convenient and simple numerical techniques for performing quantum computations based on matrix representations of Hilbert space operators are presented and illustrated by various examples. The applications include the calculations of…
We introduce quantum association schemes. This allows to define distance regular and strongly regular quantum graphs. We bring examples thereof. In addition, we formulate the duality for translation quantum association schemes corresponding…
These are notes of lectures given at UN Encuentro 2016 at the Colombia National University. We begin with the definition of infinite $W$-algebras. Then we explain the motivation for the definition if finite $W$-algebras. Then we present…
Lie groups and quantum algebras are connected through their common universal enveloping algebra. The adjoint action of Lie group on its algebra is naturally extended to related q-algebra and q-coalgebra. In such a way, quantum structure can…
The quantum even-dimensional balls are defined as the $C^*$-algebras generated by certain graphs. We exhibit a polynomial algebra for each even-dimensional quantum ball, and classify the irreducible representations of it.
We encapsulate the basic notions of the theory of vertex algebras into the construction of a comonad on an appropriate category of formal distributions. Vertex algebras are recovered as coalgebras over this comonad.
We investigate the physics of quantum reference frames. Specifically, we study several simple scenarios involving a small number of quantum particles, whereby we promote one of these particles to the role of a quantum observer and ask what…
In this note we give an introduction to the topic of quantum control, explaining what its objectives are, and describing some of its limitations.
Quantum information science is an exciting, wide, rapidly progressing, cross-disciplinary field, and that very nature makes it both attractive and hard to enter. In this primer, we first provide answers to the three essential questions that…