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Fundamental Mathematical Structures of Quantum Theory, Valter Moretti


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Автор: Valter Moretti
Название:  Fundamental Mathematical Structures of Quantum Theory
ISBN: 9783030183455
Издательство: Springer
Классификация:


ISBN-10: 3030183459
Обложка/Формат: Hardcover
Страницы: 337
Вес: 0.69 кг.
Дата издания: 2019
Язык: English
Издание: 1st ed. 2019
Иллюстрации: 1 illustrations, black and white; xiii, 337 p. 1 illus.
Размер: 234 x 156 x 21
Читательская аудитория: Professional & vocational
Основная тема: Physics
Подзаголовок: Spectral Theory, Foundational Issues, Symmetries, Algebraic Formulation
Ссылка на Издательство: Link
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Поставляется из: Германии
Описание: This textbook presents in a concise and self-contained way the advanced fundamental mathematical structures in quantum theory. It is based on lectures prepared for a 6 months course for MSc students. The reader is introduced to the beautiful interconnection between logic, lattice theory, general probability theory, and general spectral theory including the basic theory of von Neumann algebras and of the algebraic formulation, naturally arising in the study of the mathematical machinery of quantum theories. Some general results concerning hidden-variable interpretations of QM such as Gleasons and the Kochen-Specker theorems and the related notions of realism and non-contextuality are carefully discussed. This is done also in relation with the famous Bell (BCHSH) inequality concerning local causality.Written in a didactic style, this book includes many examples and solved exercises.The work is organized as follows. Chapter 1 reviews some elementary facts and properties of quantum systems. Chapter 2 and 3 present the main results of spectral analysis in complex Hilbert spaces. Chapter 4 introduces the point of view of the orthomodular lattices theory. Quantum theory form this perspective turns out to the probability measure theory on the non-Boolean lattice of elementary observables and Gleasons theorem characterizes all these measures. Chapter 5 deals with some philosophical and interpretative aspects of quantum theory like hidden-variable formulations of QM. The Kochen-Specker theorem and its implications are analyzed also in relation BCHSH inequality, entanglement, realism, locality, and non-contextuality. Chapter 6 focuses on the algebra of observables also in the presence of superselection rules introducing the notion of von Neumann algebra. Chapter 7 offers the idea of (groups of) quantum symmetry, in particular, illustrated in terms of Wigner and Kadison theorems. Chapter 8 deals with the elementary ideas and results of the so called algebraic formulation of quantum theories in terms of both *-algebras and C*-algebras.This book should appeal to a dual readership: on one hand mathematicians that wish to acquire the tools that unlock the physical aspects of quantum theories; on the other physicists eager to solidify their understanding of the mathematical scaffolding of quantum theories.

Дополнительное описание: General Phenomenology of the Quantum World and Elementary Formalism.- Hilbert Spaces and Classes of Operators.- Observables and States in General Hilbert Spaces: Spectral Theory.- Fundamental Quantum Structures on Hilbert Spaces.- Realism, Non-Contextuali



Quantum Systems, Channels, Information: A Mathematical Introduction

Автор: Alexander S. Holevo
Название: Quantum Systems, Channels, Information: A Mathematical Introduction
ISBN: 311027325X ISBN-13(EAN): 9783110273250
Издательство: Walter de Gruyter
Цена: 16916.00 р. 24166.00 -30%
Наличие на складе: Есть (1 шт.)
Описание: The main emphasis of this work is the mathematical theory of quantum channels and their entropic and information characteristics. Quantum information theory is one of the key research areas, since it leads the way to vastly increased computing speeds by using quantum systems to store and process information. Quantum cryptography allows for secure communication of classified information. Research in the field of quantum informatics, including quantum information theory, is in progress in leading scientific centers throughout the world.The past years were marked with impressive progress made by several researchers in solution of some difficult problems, in particular, the additivity of the entropy characteristics of quantum channels. This suggests a need for a book that not only introduces the basic concepts of quantum information theory, but also presents in detail some of the latest achievements.

Geometry of Quantum States

Автор: Bengtsson Ingemar
Название: Geometry of Quantum States
ISBN: 1107026253 ISBN-13(EAN): 9781107026254
Издательство: Cambridge Academ
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Цена: 13779.00 р.
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Описание: The second edition of a book that has become a standard reference for researchers working on geometric aspects of quantum entanglement and quantum theory of information. Its comprehensive style makes it suitable for students of physics, information science, and mathematics wishing to learn more about quantum mechanics and quantum entanglement.

Logic and Algebraic Structures in Quantum Computing

Автор: Chubb
Название: Logic and Algebraic Structures in Quantum Computing
ISBN: 110703339X ISBN-13(EAN): 9781107033399
Издательство: Cambridge Academ
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Цена: 21226.00 р.
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Описание: In this international cross-disciplinary collaboration, leading experts explore connections across their respective fields. The book offers an insight into the fundamental questions in quantum theory and logic, which will appeal to many researchers and graduate students including logicians, mathematicians, computer scientists, and physicists.

Fifty Years Of Mathematical Physics: Selected Works Of Ludwig Faddeev

Автор: Ge Mo-Lin Et Al
Название: Fifty Years Of Mathematical Physics: Selected Works Of Ludwig Faddeev
ISBN: 9813109335 ISBN-13(EAN): 9789813109339
Издательство: World Scientific Publishing
Цена: 12012.00 р.
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Описание: This Unique Volume Summarizes With A Historical Perspective Several Of The Major Scientific Achievements Of Ludwig Faddeev, With A Foreword By Nobel Laureate C N Yang. The Volume That Spans Over Fifty Years Of Faddeev'S Career Begins Where He Started His Own Scientific Research, In The Subject Of Scattering Theory And The Three-Body Problem. It Then Continues To Describe Faddeev'S Contributions To Automorphic Functions, Followed By An Extensive Account Of His Many Fundamental Contributions To Quantum Field Theory Including His Original Article On Ghosts With Popov. Faddeev'S Contributions To Soliton Theory And Integrable Models Are Then Described, Followed By A Survey Of His Work On Quantum Groups. The Final Scientific Section Is Devoted To Faddeev'S Contemporary Research Including Articles On His Long-Term Interest In Constructing Knotted Solitons And Understanding Confinement. The Volume Concludes With His Personal View On Science And Mathematical Physics In Particular.

First Course In Integral Equations, A (Second Edition)

Автор: Wazwaz Abdul-Majid
Название: First Course In Integral Equations, A (Second Edition)
ISBN: 9814675121 ISBN-13(EAN): 9789814675123
Издательство: World Scientific Publishing
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Цена: 6336.00 р.
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Описание: This second edition integrates the newly developed methods with classical techniques to give both modern and powerful approaches for solving integral equations.

The theory of quantum information

Автор: Watrous, John (university Of Waterloo, Ontario)
Название: The theory of quantum information
ISBN: 1107180562 ISBN-13(EAN): 9781107180567
Издательство: Cambridge Academ
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Цена: 11563.00 р.
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Описание: Intended for graduate students and researchers, this book presents a formal development of the mathematical theory of quantum information. Largely self-contained, with clear proofs and a wide range of exercises, it will help the reader grasp the fundamental facts and techniques that form the mathematical foundations of the subject.

Fundamental Directions in Mathematical Fluid Mechanics

Автор: Giovanni P. Galdi; John G. Heywood; Rolf Rannacher
Название: Fundamental Directions in Mathematical Fluid Mechanics
ISBN: 3034895615 ISBN-13(EAN): 9783034895613
Издательство: Springer
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Цена: 13974.00 р.
Наличие на складе: Есть у поставщика Поставка под заказ.

Описание: This volume consists of six articles, each treating an important topic in the theory ofthe Navier-Stokes equations, at the research level. At that time it was decided that this volume should be published in association with the journal, and expanded to include articles by J.

Mean Field Theories and Dual Variation - Mathematical Structures of the Mesoscopic Model

Автор: Takashi Suzuki
Название: Mean Field Theories and Dual Variation - Mathematical Structures of the Mesoscopic Model
ISBN: 946239153X ISBN-13(EAN): 9789462391536
Издательство: Springer
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Цена: 13275.00 р.
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Описание: The aim of this book is to formulate the variational and hierarchical aspects of the equations that arise in the mean field theory from macroscopic profiles to microscopic principles, from dynamics to equilibrium, and from biological models to models that arise from chemistry and physics.

Mathematical Theory of Elastic Structures

Автор: Kang Feng; Zhong-Ci Shi
Название: Mathematical Theory of Elastic Structures
ISBN: 3662032880 ISBN-13(EAN): 9783662032886
Издательство: Springer
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Цена: 6986.00 р.
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Описание: The finite element method, which was independently created and developed in different ways by sci- entists both in China and in the West, is a kind of systematic and modern numerical method for solving partial differential equations, especially el- liptic equations.

Nonlinear Systems and Their Remarkable Mathematical Structures

Название: Nonlinear Systems and Their Remarkable Mathematical Structures
ISBN: 1138601004 ISBN-13(EAN): 9781138601000
Издательство: Taylor&Francis
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Цена: 33686.00 р.
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Описание: The book aims to describe some recent progress in nonlinear differential equations and nonlinear dynamical systems (both continuous and discrete).

Mathematical Modelling for Next-Generation Cryptography

Автор: Tsuyoshi Takagi; Masato Wakayama; Keisuke Tanaka;
Название: Mathematical Modelling for Next-Generation Cryptography
ISBN: 9811353093 ISBN-13(EAN): 9789811353093
Издательство: Springer
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Цена: 15372.00 р.
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Описание:

This book presents the mathematical background underlying security modeling in the context of next-generation cryptography. By introducing new mathematical results in order to strengthen information security, while simultaneously presenting fresh insights and developing the respective areas of mathematics, it is the first-ever book to focus on areas that have not yet been fully exploited for cryptographic applications such as representation theory and mathematical physics, among others.
Recent advances in cryptanalysis, brought about in particular by quantum computation and physical attacks on cryptographic devices, such as side-channel analysis or power analysis, have revealed the growing security risks for state-of-the-art cryptographic schemes. To address these risks, high-performance, next-generation cryptosystems must be studied, which requires the further development of the mathematical background of modern cryptography. More specifically
, in order to avoid the security risks posed by adversaries with advanced attack capabilities, cryptosystems must be upgraded, which in turn relies on a wide range of mathematical theories.
This book is suitable for use in an advanced graduate course in mathematical cryptography, while also offering a valuable reference guide for experts.

Автор: Palash B. Pal
Название: A Physicist`s Introduction to Algebraic Structures: Vector Spaces, Groups, Topological Spaces and More
ISBN: 1108729118 ISBN-13(EAN): 9781108729116
Издательство: Cambridge Academ
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Цена: 11086.00 р.
Наличие на складе: Поставка под заказ.

Описание: An algebraic structure consists of a set of elements, with some rule of combining them, or some special property of selected subsets of the entire set. Many algebraic structures, such as vector space and group, come to everyday use of a modern physicist. Catering to the needs of graduate students and researchers in the field of mathematical physics and theoretical physics, this comprehensive and valuable text discusses the essential concepts of algebraic structures such as metric space, group, modular numbers, algebraic integers, field, vector space, Boolean algebra, measure space and Lebesgue integral. Important topics including finite and infinite dimensional vector spaces, finite groups and their representations, unitary groups and their representations and representations of the Lorentz group, homotopy and homology of topological spaces are covered extensively. Rich pedagogy includes various problems interspersed throughout the book for better understanding of concepts.


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