Quantum Mathematical Physics

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Quantum Mathematical Physics

Quantum Mathematical Physics Pdf/ePub eBook Author: ,
Editor: Springer Science & Business Media
ISBN: 3662050080
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Quantum Mathematical Physics by , Summary

This book is a new edition of Volumes 3 and 4 of Walter Thirring’s famous textbook on mathematical physics. The first part is devoted to quantum mechanics and especially to its applications to scattering theory, atoms and molecules. The second part deals with quantum statistical mechanics examining fundamental concepts like entropy, ergodicity and thermodynamic functions.

Quantum Mathematical Physics

Quantum Mathematical Physics Pdf/ePub eBook Author: Felix Finster,Johannes Kleiner,Christian Röken,Jürgen Tolksdorf
Editor: Birkhäuser
ISBN: 331926902X
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Quantum Mathematical Physics by Felix Finster,Johannes Kleiner,Christian Röken,Jürgen Tolksdorf Summary

Quantum physics has been highly successful for more than 90 years. Nevertheless, a rigorous construction of interacting quantum field theory is still missing. Moreover, it is still unclear how to combine quantum physics and general relativity in a unified physical theory. Attacking these challenging problems of contemporary physics requires highly advanced mathematical methods as well as radically new physical concepts. This book presents different physical ideas and mathematical approaches in this direction. It contains a carefully selected cross-section of lectures which took place in autumn 2014 at the sixth conference ``Quantum Mathematical Physics - A Bridge between Mathematics and Physics'' in Regensburg, Germany. In the tradition of the other proceedings covering this series of conferences, a special feature of this book is the exposition of a wide variety of approaches, with the intention to facilitate a comparison. The book is mainly addressed to mathematicians and physicists who are interested in fundamental questions of mathematical physics. It allows the reader to obtain a broad and up-to-date overview of a fascinating active research area.

A Course in Mathematical Physics 3

A Course in Mathematical Physics 3 Pdf/ePub eBook Author: Walter Thirring
Editor: Springer Science & Business Media
ISBN: 3709175232
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A Course in Mathematical Physics 3 by Walter Thirring Summary

In this third volume of A Course in Mathematical Physics I have attempted not simply to introduce axioms and derive quantum mechanics from them, but also to progress to relevant applications. Reading the axiomatic litera ture often gives one the impression that it largely consists of making refined axioms, thereby freeing physics from any trace of down-to-earth residue and cutting it off from simpler ways of thinking. The goal pursued here, however, is to come up with concrete results that can be compared with experimental facts. Everything else should be regarded only as a side issue, and has been chosen for pragmatic reasons. It is precisely with this in mind that I feel it appropriate to draw upon the most modern mathematical methods. Only by their means can the logical fabric of quantum theory be woven with a smooth structure; in their absence, rough spots would . inevitably appear, especially in the theory of unbounded operators, where the details are too intricate to be comprehended easily. Great care has been taken to build up this mathematical weaponry as completely as possible, as it is also the basic arsenal of the next volume. This means that many proofs have been tucked away in the exercises. My greatest concern was to replace the ordinary cal culations of uncertain accuracy with better ones having error bounds, in order to raise the crude manners of theoretical physics to the more cultivated level of experimental physics.

Mathematics of Classical and Quantum Physics

Mathematics of Classical and Quantum Physics Pdf/ePub eBook Author: Frederick W. Byron,Robert W. Fuller
Editor: Courier Corporation
ISBN: 0486135063
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Mathematics of Classical and Quantum Physics by Frederick W. Byron,Robert W. Fuller Summary

Graduate-level text offers unified treatment of mathematics applicable to many branches of physics. Theory of vector spaces, analytic function theory, theory of integral equations, group theory, and more. Many problems. Bibliography.

Quantum Theory

Quantum Theory Pdf/ePub eBook Author: Peter Bongaarts
Editor: Springer
ISBN: 3319095617
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Quantum Theory by Peter Bongaarts Summary

This book was inspired by the general observation that the great theories of modern physics are based on simple and transparent underlying mathematical structures – a fact not usually emphasized in standard physics textbooks – which makes it easy for mathematicians to understand their basic features. It is a textbook on quantum theory intended for advanced undergraduate or graduate students: mathematics students interested in modern physics, and physics students who are interested in the mathematical background of physics and are dissatisfied with the level of rigor in standard physics courses. More generally, it offers a valuable resource for all mathematicians interested in modern physics, and all physicists looking for a higher degree of mathematical precision with regard to the basic concepts in their field.

Quantum Theory for Mathematicians

Quantum Theory for Mathematicians Pdf/ePub eBook Author: Brian C. Hall
Editor: Springer Science & Business Media
ISBN: 1461471168
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Quantum Theory for Mathematicians by Brian C. Hall Summary

Although ideas from quantum physics play an important role in many parts of modern mathematics, there are few books about quantum mechanics aimed at mathematicians. This book introduces the main ideas of quantum mechanics in language familiar to mathematicians. Readers with little prior exposure to physics will enjoy the book's conversational tone as they delve into such topics as the Hilbert space approach to quantum theory; the Schrödinger equation in one space dimension; the Spectral Theorem for bounded and unbounded self-adjoint operators; the Stone–von Neumann Theorem; the Wentzel–Kramers–Brillouin approximation; the role of Lie groups and Lie algebras in quantum mechanics; and the path-integral approach to quantum mechanics. The numerous exercises at the end of each chapter make the book suitable for both graduate courses and independent study. Most of the text is accessible to graduate students in mathematics who have had a first course in real analysis, covering the basics of L2 spaces and Hilbert spaces. The final chapters introduce readers who are familiar with the theory of manifolds to more advanced topics, including geometric quantization.

Hilbert Space Operators in Quantum Physics

Hilbert Space Operators in Quantum Physics Pdf/ePub eBook Author: Jirí Blank,Pavel Exner,Miloslav Havlícek
Editor: Springer Science & Business Media
ISBN: 1402088701
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Hilbert Space Operators in Quantum Physics by Jirí Blank,Pavel Exner,Miloslav Havlícek Summary

The new edition of this book detailing the theory of linear-Hilbert space operators and their use in quantum physics contains two new chapters devoted to properties of quantum waveguides and quantum graphs. The bibliography contains 130 new items.

Local Quantum Physics

Local Quantum Physics Pdf/ePub eBook Author: Rudolf Haag
Editor: Springer Science & Business Media
ISBN: 3642614582
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Local Quantum Physics by Rudolf Haag Summary

The new edition provided the opportunity of adding a new chapter entitled "Principles and Lessons of Quantum Physics". It was a tempting challenge to try to sharpen the points at issue in the long lasting debate on the Copenhagen Spirit, to assess the significance of various arguments from our present vantage point, seventy years after the advent of quantum theory, where, after ali, some problems appear in a different light. It includes a section on the assumptions leading to the specific mathematical formalism of quantum theory and a section entitled "The evolutionary picture" describing my personal conclusions. Alto gether the discussion suggests that the conventional language is too narrow and that neither the mathematical nor the conceptual structure are built for eter nity. Future theories will demand radical changes though not in the direction of a return to determinism. Essential lessons taught by Bohr will persist. This chapter is essentially self-contained. Some new material has been added in the last chapter. It concerns the char acterization of specific theories within the general frame and recent progress in quantum field theory on curved space-time manifolds. A few pages on renor malization have been added in Chapter II and some effort has been invested in the search for mistakes and unclear passages in the first edition. The central objective of the book, expressed in the title "Local Quantum Physics", is the synthesis between special relativity and quantum theory to gether with a few other principles of general nature.

Quantum Information Processing with Finite Resources

Quantum Information Processing with Finite Resources Pdf/ePub eBook Author: Marco Tomamichel
Editor: Springer
ISBN: 3319218913
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Quantum Information Processing with Finite Resources by Marco Tomamichel Summary

This book provides the reader with the mathematical framework required to fully explore the potential of small quantum information processing devices. As decoherence will continue to limit their size, it is essential to master the conceptual tools which make such investigations possible. A strong emphasis is given to information measures that are essential for the study of devices of finite size, including Rényi entropies and smooth entropies. The presentation is self-contained and includes rigorous and concise proofs of the most important properties of these measures. The first chapters will introduce the formalism of quantum mechanics, with particular emphasis on norms and metrics for quantum states. This is necessary to explore quantum generalizations of Rényi divergence and conditional entropy, information measures that lie at the core of information theory. The smooth entropy framework is discussed next and provides a natural means to lift many arguments from information theory to the quantum setting. Finally selected applications of the theory to statistics and cryptography are discussed. The book is aimed at graduate students in Physics and Information Theory. Mathematical fluency is necessary, but no prior knowledge of quantum theory is required.

General Principles of Quantum Field Theory

General Principles of Quantum Field Theory Pdf/ePub eBook Author: N.N. Bogolubov,Anatoly A. Logunov,A.I. Oksak,I. Todorov
Editor: Springer Science & Business Media
ISBN: 9400904916
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General Principles of Quantum Field Theory by N.N. Bogolubov,Anatoly A. Logunov,A.I. Oksak,I. Todorov Summary

The majority of the "memorable" results of relativistic quantum theory were obtained within the framework of the local quantum field approach. The explanation of the basic principles of the local theory and its mathematical structure has left its mark on all modern activity in this area. Originally, the axiomatic approach arose from attempts to give a mathematical meaning to the quantum field theory of strong interactions (of Yukawa type). The fields in such a theory are realized by operators in Hilbert space with a positive Poincare-invariant scalar product. This "classical" part of the axiomatic approach attained its modern form as far back as the sixties. * It has retained its importance even to this day, in spite of the fact that nowadays the main prospects for the description of the electro-weak and strong interactions are in connection with the theory of gauge fields. In fact, from the point of view of the quark model, the theory of strong interactions of Wightman type was obtained by restricting attention to just the "physical" local operators (such as hadronic fields consisting of ''fundamental'' quark fields) acting in a Hilbert space of physical states. In principle, there are enough such "physical" fields for a description of hadronic physics, although this means that one must reject the traditional local Lagrangian formalism. (The connection is restored in the approximation of low-energy "phe nomenological" Lagrangians.

A Course in Mathematical Physics

A Course in Mathematical Physics Pdf/ePub eBook Author: Walter Thirring
Editor: Springer Science & Business Media
ISBN: 3709175267
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A Course in Mathematical Physics by Walter Thirring Summary

In this final volume I have tried to present the subject of statistical mechanics in accordance with the basic principles of the series. The effort again entailed following Gustav Mahler's maxim, "Tradition = Schlamperei" (i.e., filth) and clearing away a large portion of this tradition-laden area. The result is a book with little in common with most other books on the subject. The ordinary perturbation-theoretic calculations are not very useful in this field. Those methods have never led to propositions of much substance. Even when perturbation series, which for the most part never converge, can be given some asymptotic meaning, it cannot be determined how close the nth order approximation comes to the exact result. Since analytic solutions of nontrivial problems are beyond human capabilities, for better or worse we must settle for sharp bounds on the quantities of interest, and can at most strive to make the degree of accuracy satisfactory.

Mathematical Physics of Quantum Mechanics

Mathematical Physics of Quantum Mechanics Pdf/ePub eBook Author: Joachim Asch,Alain Joye
Editor: Springer
ISBN: 3540342737
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Mathematical Physics of Quantum Mechanics by Joachim Asch,Alain Joye Summary

This selection of outstanding articles – an outgrowth of the QMath9 meeting for young scientists – covers new techniques and recent results on spectral theory, statistical mechanics, Bose-Einstein condensation, random operators, magnetic Schrödinger operators and more. The book’s pedagogical style makes it a useful introduction to the research literature for postgraduate students. For more expert researchers it will serve as a concise source of modern reference.

Mathematical Theory of Quantum Fields

Mathematical Theory of Quantum Fields Pdf/ePub eBook Author: Huzihiro Araki
Editor: Oxford University Press
ISBN: 0192539116
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Mathematical Theory of Quantum Fields by Huzihiro Araki Summary

This is an introduction to the mathematical foundations of quantum field theory, using operator algebraic methods and emphasizing the link between the mathematical formulations and related physical concepts. It starts with a general probabilistic description of physics, which encompasses both classical and quantum physics. The basic key physical notions are clarified at this point. It then introduces operator algebraic methods for quantum theory, and goes on to discuss the theory of special relativity, scattering theory, and sector theory in this context.

Geometric Phases in Classical and Quantum Mechanics

Geometric Phases in Classical and Quantum Mechanics Pdf/ePub eBook Author: Dariusz Chruscinski,Andrzej Jamiolkowski
Editor: Springer Science & Business Media
ISBN: 0817681760
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Geometric Phases in Classical and Quantum Mechanics by Dariusz Chruscinski,Andrzej Jamiolkowski Summary

Several well-established geometric and topological methods are used in this work in an application to a beautiful physical phenomenon known as the geometric phase. This book examines the geometric phase, bringing together different physical phenomena under a unified mathematical scheme. The material is presented so that graduate students and researchers in applied mathematics and physics with an understanding of classical and quantum mechanics can handle the text.

Mathematical Concepts of Quantum Mechanics

Mathematical Concepts of Quantum Mechanics Pdf/ePub eBook Author: Stephen J. Gustafson,Israel Michael Sigal
Editor: Springer
ISBN: 3642557295
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Mathematical Concepts of Quantum Mechanics by Stephen J. Gustafson,Israel Michael Sigal Summary

The book gives a streamlined introduction to quantum mechanics and describes the basic mathematical structures underpinning it. From the reviews: "This book is an introduction to the mathematics of quantum mechanics....The strength of the book is where it shows how the mathematical treatment of quantum mechanics brings insights to physics....It will be useful to the experienced reader as a guide to the impressive recent advances in mathematical quantum mechanics." --SIAM REVIEW

Quantum Information Theory and Quantum Statistics

Quantum Information Theory and Quantum Statistics Pdf/ePub eBook Author: Dénes Petz
Editor: Springer Science & Business Media
ISBN: 3540746366
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Quantum Information Theory and Quantum Statistics by Dénes Petz Summary

This concise and readable book addresses primarily readers with a background in classical statistical physics and introduces quantum mechanical notions as required. Conceived as a primer to bridge the gap between statistical physics and quantum information, it emphasizes concepts and thorough discussions of the fundamental notions and prepares the reader for deeper studies, not least through a selection of well chosen exercises.

Mathematical Topics Between Classical and Quantum Mechanics

Mathematical Topics Between Classical and Quantum Mechanics Pdf/ePub eBook Author: Nicholas P. Landsman
Editor: Springer Science & Business Media
ISBN: 146121680X
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Mathematical Topics Between Classical and Quantum Mechanics by Nicholas P. Landsman Summary

This monograph draws on two traditions: the algebraic formulation of quantum mechanics as well as quantum field theory, and the geometric theory of classical mechanics. These are combined in a unified treatment of the theory of Poisson algebras of observables and pure state spaces with a transition probability, which leads on to a discussion of the theory of quantization and the classical limit from this perspective. A prototype of quantization comes from the analogy between the C*- algebra of a Lie groupoid and the Poisson algebra of the corresponding Lie algebroid. The parallel between reduction of symplectic manifolds in classical mechanics and induced representations of groups and C*- algebras in quantum mechanics plays an equally important role. Examples from physics include constrained quantization, curved spaces, magnetic monopoles, gauge theories, massless particles, and $theta$- vacua. Accessible to mathematicians with some prior knowledge of classical and quantum mechanics, and to mathematical physicists and theoretical physicists with some background in functional analysis.

Algebraic Methods in Quantum Chemistry and Physics

Algebraic Methods in Quantum Chemistry and Physics Pdf/ePub eBook Author: Francisco M. Fernandez,E.A. Castro
Editor: CRC Press
ISBN: 1000714845
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Algebraic Methods in Quantum Chemistry and Physics by Francisco M. Fernandez,E.A. Castro Summary

Algebraic Methods in Quantum Chemistry and Physics provides straightforward presentations of selected topics in theoretical chemistry and physics, including Lie algebras and their applications, harmonic oscillators, bilinear oscillators, perturbation theory, numerical solutions of the Schrödinger equation, and parameterizations of the time-evolution operator. The mathematical tools described in this book are presented in a manner that clearly illustrates their application to problems arising in theoretical chemistry and physics. The application techniques are carefully explained with step-by-step instructions that are easy to follow, and the results are organized to facilitate both manual and numerical calculations. Algebraic Methods in Quantum Chemistry and Physics demonstrates how to obtain useful analytical results with elementary algebra and calculus and an understanding of basic quantum chemistry and physics.

Quantum Mechanics

Quantum Mechanics Pdf/ePub eBook Author: Leonard Susskind,Art Friedman
Editor: Basic Books
ISBN: 0465080618
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Quantum Mechanics by Leonard Susskind,Art Friedman Summary

First he taught you classical mechanics. Now, physicist Leonard Susskind has teamed up with data engineer Art Friedman to present the theory and associated mathematics of the strange world of quantum mechanics. In this follow-up to the New York Times best-selling The Theoretical Minimum, Susskind and Friedman provide a lively introduction to this famously difficult field, which attempts to understand the behavior of sub-atomic objects through mathematical abstractions. Unlike other popularizations that shy away from quantum mechanics' weirdness, Quantum Mechanics embraces the utter strangeness of quantum logic. The authors offer crystal-clear explanations of the principles of quantum states, uncertainty and time dependence, entanglement, and particle and wave states, among other topics, and each chapter includes exercises to ensure mastery of each area. Like The Theoretical Minimum, this volume runs parallel to Susskind's eponymous Stanford University-hosted continuing education course. An approachable yet rigorous introduction to a famously difficult topic, Quantum Mechanics provides a tool kit for amateur scientists to learn physics at their own pace.