Quantum Mathematical Physics

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Quantum Mathematical Physics

Quantum Mathematical Physics [Pdf/ePub] eBook ISBN-10: 3662050080
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Publisher: Springer Science & Business Media
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Quantum Mathematical Physics by Book Resume:

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 ISBN-10: 331926902X
Author: Felix Finster,Johannes Kleiner,Christian Röken,Jürgen Tolksdorf
Publisher: Birkhäuser
File Size: 906 KB
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Quantum Mathematical Physics by Felix Finster,Johannes Kleiner,Christian Röken,Jürgen Tolksdorf Book Resume:

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.

Mathematics of Classical and Quantum Physics

Mathematics of Classical and Quantum Physics [Pdf/ePub] eBook ISBN-10: 0486135063
Author: Frederick W. Byron,Robert W. Fuller
Publisher: Courier Corporation
File Size: 993 KB
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Mathematics of Classical and Quantum Physics by Frederick W. Byron,Robert W. Fuller Book Resume:

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.

A Course in Mathematical Physics 3

A Course in Mathematical Physics 3 [Pdf/ePub] eBook ISBN-10: 3709175232
Author: Walter Thirring
Publisher: Springer Science & Business Media
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A Course in Mathematical Physics 3 by Walter Thirring Book Resume:

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.

Quantum Theory

Quantum Theory [Pdf/ePub] eBook ISBN-10: 3319095617
Author: Peter Bongaarts
Publisher: Springer
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Quantum Theory by Peter Bongaarts Book Resume:

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.

Hilbert Space Operators in Quantum Physics

Hilbert Space Operators in Quantum Physics [Pdf/ePub] eBook ISBN-10: 1402088701
Author: Jirí Blank,Pavel Exner,Miloslav Havlícek
Publisher: Springer Science & Business Media
File Size: 1016 KB
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Hilbert Space Operators in Quantum Physics by Jirí Blank,Pavel Exner,Miloslav Havlícek Book Resume:

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.

Mathematical Physics of Quantum Mechanics

Mathematical Physics of Quantum Mechanics [Pdf/ePub] eBook ISBN-10: 3540342737
Author: Joachim Asch,Alain Joye
Publisher: Springer
File Size: 833 KB
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Mathematical Physics of Quantum Mechanics by Joachim Asch,Alain Joye Book Resume:

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.

A Course in Mathematical Physics

A Course in Mathematical Physics [Pdf/ePub] eBook ISBN-10: 3709175267
Author: Walter Thirring
Publisher: Springer Science & Business Media
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A Course in Mathematical Physics by Walter Thirring Book Resume:

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.

Local Quantum Physics

Local Quantum Physics [Pdf/ePub] eBook ISBN-10: 3642614582
Author: Rudolf Haag
Publisher: Springer Science & Business Media
File Size: 451 KB
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Local Quantum Physics by Rudolf Haag Book Resume:

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 Field Theory I: Basics in Mathematics and Physics

Quantum Field Theory I: Basics in Mathematics and Physics [Pdf/ePub] eBook ISBN-10: 354034764X
Author: Eberhard Zeidler
Publisher: Springer Science & Business Media
File Size: 1923 KB
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Quantum Field Theory I: Basics in Mathematics and Physics by Eberhard Zeidler Book Resume:

This is the first volume of a modern introduction to quantum field theory which addresses both mathematicians and physicists, at levels ranging from advanced undergraduate students to professional scientists. The book bridges the acknowledged gap between the different languages used by mathematicians and physicists. For students of mathematics the author shows that detailed knowledge of the physical background helps to motivate the mathematical subjects and to discover interesting interrelationships between quite different mathematical topics. For students of physics, fairly advanced mathematics is presented, which goes beyond the usual curriculum in physics.

General Principles of Quantum Field Theory

General Principles of Quantum Field Theory [Pdf/ePub] eBook ISBN-10: 9400904916
Author: N.N. Bogolubov,Anatoly A. Logunov,A.I. Oksak,I. Todorov
Publisher: Springer Science & Business Media
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General Principles of Quantum Field Theory by N.N. Bogolubov,Anatoly A. Logunov,A.I. Oksak,I. Todorov Book Resume:

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.

Topics in Quantum Mechanics

Topics in Quantum Mechanics [Pdf/ePub] eBook ISBN-10: 1461200091
Author: Floyd Williams
Publisher: Springer Science & Business Media
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Topics in Quantum Mechanics by Floyd Williams Book Resume:

This self-contained text presents quantum mechanics from the point of view of some computational examples with a mixture of mathematical clarity often not found in texts offering only a purely physical point of view. Emphasis is placed on the systematic application of the Nikiforov-- Uvarov theory of generalized hypergeometric differential equations to solve the Schr"dinger equation and to obtain the quantization of energies from a single unified point of view.

Advances in Algebraic Quantum Field Theory

Advances in Algebraic Quantum Field Theory [Pdf/ePub] eBook ISBN-10: 3319213539
Author: Romeo Brunetti,Claudio Dappiaggi,Klaus Fredenhagen,Jakob Yngvason
Publisher: Springer
File Size: 1737 KB
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Read Count: 837991

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Advances in Algebraic Quantum Field Theory by Romeo Brunetti,Claudio Dappiaggi,Klaus Fredenhagen,Jakob Yngvason Book Resume:

This text focuses on the algebraic formulation of quantum field theory, from the introductory aspects to the applications to concrete problems of physical interest. The book is divided in thematic chapters covering both introductory and more advanced topics. These include the algebraic, perturbative approach to interacting quantum field theories, algebraic quantum field theory on curved spacetimes (from its structural aspects to the applications in cosmology and to the role of quantum spacetimes), algebraic conformal field theory, the Kitaev's quantum double model from the point of view of local quantum physics and constructive aspects in relation to integrable models and deformation techniques. The book is addressed to master and graduate students both in mathematics and in physics, who are interested in learning the structural aspects and the applications of algebraic quantum field theory.

Mathematical Theory of Quantum Fields

Mathematical Theory of Quantum Fields [Pdf/ePub] eBook ISBN-10: 0192539116
Author: Huzihiro Araki
Publisher: Oxford University Press
File Size: 1720 KB
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Mathematical Theory of Quantum Fields by Huzihiro Araki Book Resume:

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 ISBN-10: 0817681760
Author: Dariusz Chruscinski,Andrzej Jamiolkowski
Publisher: Springer Science & Business Media
File Size: 1825 KB
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Read Count: 2878315

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Geometric Phases in Classical and Quantum Mechanics by Dariusz Chruscinski,Andrzej Jamiolkowski Book Resume:

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.

Quantum Information Processing with Finite Resources

Quantum Information Processing with Finite Resources [Pdf/ePub] eBook ISBN-10: 3319218913
Author: Marco Tomamichel
Publisher: Springer
File Size: 1918 KB
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Quantum Information Processing with Finite Resources by Marco Tomamichel Book Resume:

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.

Mathematical Topics Between Classical and Quantum Mechanics

Mathematical Topics Between Classical and Quantum Mechanics [Pdf/ePub] eBook ISBN-10: 146121680X
Author: Nicholas P. Landsman
Publisher: Springer Science & Business Media
File Size: 594 KB
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Mathematical Topics Between Classical and Quantum Mechanics by Nicholas P. Landsman Book Resume:

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.

A Mathematical Primer on Quantum Mechanics

A Mathematical Primer on Quantum Mechanics [Pdf/ePub] eBook ISBN-10: 3319778935
Author: Alessandro Teta
Publisher: Springer
File Size: 839 KB
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A Mathematical Primer on Quantum Mechanics by Alessandro Teta Book Resume:

This book offers a rigorous yet elementary approach to quantum mechanics that will meet the needs of Master’s-level Mathematics students and is equally suitable for Physics students who are interested in gaining a deeper understanding of the mathematical structure of the theory. Throughout the coverage, which is limited to single-particle quantum mechanics, the focus is on formulating theory and developing applications in a mathematically precise manner. Following a review of selected key concepts in classical physics and the historical background, the basic elements of the theory of operators in Hilbert spaces are presented and used to formulate the rules of quantum mechanics. The discussion then turns to free particles, harmonic oscillators, delta potential, and hydrogen atoms, providing rigorous proofs of the corresponding dynamical properties. Starting from an analysis of these applications, readers are subsequently introduced to more advanced topics such as the classical limit, scattering theory, and spectral analysis of Schrödinger operators. The main content is complemented by numerous exercises that stimulate interactive learning and help readers check their progress.

Quantum Information Theory and Quantum Statistics

Quantum Information Theory and Quantum Statistics [Pdf/ePub] eBook ISBN-10: 3540746366
Author: Dénes Petz
Publisher: Springer Science & Business Media
File Size: 1926 KB
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Read Count: 9046620

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Quantum Information Theory and Quantum Statistics by Dénes Petz Book Resume:

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.