Related papers: Quantum Gauge Theories
We review the present status of gauge theories built on various quantum space-times described by noncommutative space-times. The mathematical tools and notions underlying their construction are given. Different formulations of gauge theory…
Formulating gauge theories on a lattice offers a genuinely non-perturbative way of studying quantum field theories, and has led to impressive achievements. In particular, it significantly deepened our understanding of quantum…
The goal of this article is to present an introduction to loop quantum gravity -a background independent, non-perturbative approach to the problem of unification of general relativity and quantum physics, based on a quantum theory of…
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…
We explore a field theoretical approach to quantum computing and control. This book consists of three parts. The basics of systems theory and field theory are reviewed in Part I. In Part II, a gauge theory is reinterpreted from a systems…
Some very elementary ideas about quantum groups and quantum algebras are introduced and a few examples of their physical applications are mentioned.
In this review we attempt to present an overview of some of the better known quantization techniques found in the current literature and used both by physicists and mathematicians. The treatment is more descriptive than rigorous, for we aim…
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…
We introduce the key ideas behind the group field theory approach to quantum gravity, and the basic elements of its formalism. We also briefly report on some recent results obtained in this approach, concerning both the mathematical…
Recent advances in cooling, control, and measurement of mechanical systems in the quantum regime have opened the possibility of the first direct observation of quantum gravity, at scales achievable in experiments. This paper gives a broad…
We develop a generalised gauge theory in which the role of gauge group is played by a coalgebra and the role of principal bundle by an algebra. The theory provides a unifying point of view which includes quantum group gauge theory,…
This is an introduction to the group field theory approach to quantum gravity, with emphasis on motivations and basic formalism, more than on recent results; we elaborate on the various ingredients, both conceptual and formal, of the…
After a long technical and consequently philosophical disgression about the necessity of the construction presented in this book, a logically consistent and precise theory of quantum gravity is presented. The construction of this theory…
In the last few years, theoretical study of quantum systems serving as computational devices has achieved tremendous progress. We now have strong theoretical evidence that quantum computers, if built, might be used as a dramatically…
In this work, we present a brief but insightful overview of the gauge theories, which are defined on $ n $-dimensional lattices by using finite gauge groups, in order to show how they can be interpreted as a Hamiltonian system with…
The purpose of this text is to set up a few basic notions concerning quantum graphs, to indicate some areas addressed in the quantum graph research, and to provide some pointers to the literature. The pointers in many cases are secondary,…
A unified framework for different formulations of quantum theoery is introduced specifying what is meant by a quantum mechanical theory in general.
We introduce the group field theory formalism for quantum gravity, mainly from the point of view of loop quantum gravity, stressing its promising aspects. We outline the foundations of the formalism, survey recent results and offer a…
We present a survey of quantum algorithms, primarily for an intended audience of pure mathematicians. We place an emphasis on algorithms involving group theory.
A new picture of Quantum Mechanics based on the theory of groupoids is presented. This picture provides the mathematical background for Schwinger's algebra of selective measurements and helps to understand its scope and eventual…