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Quantum Mathematical Physics | ,

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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..

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Quantum Mathematical Physics | Felix Finster,Johannes Kleiner,Christian Röken,Jürgen Tolksdorf

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Quantum Mathematical Physics - Felix Finster,Johannes Kleiner,Christian Röken,Jürgen Tolksdorf Preview:

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..

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Mathematics of Classical and Quantum Physics | Frederick W. Byron,Robert W. Fuller

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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..

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A Course in Mathematical Physics 3 | Walter Thirring

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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..

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Mathematical Physics of Quantum Mechanics | Joachim Asch,Alain Joye

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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..

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Quantum Theory | Peter Bongaarts

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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..

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Classical Mathematical Physics | Walter Thirring

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This book combines the enlarged and corrected editions of both volumes on classical physics stemming from Thirrings famous course. The treatment of classical dynamical systems uses analysis on manifolds to provide the mathematical setting for discussions of Hamiltonian systems, canonical transformations, constants of motion, and perturbation theory. Problems discussed include: nonrelativistic motion of particles and systems, relativistic motion in electromagnetic and gravitational fields, and the structure of black holes. The treatment of classical fields uses the language of differential geometry, treating both Maxwells and Einsteins equations in a compact and clear fashion. The book includes discussions of the electromagnetic field due to known charge distributions and in the presence of conductors, as well as a new section on gauge theories. It discusses the solutions of the Einstein equations for maximally symmetric spaces and spaces with maximally symmetric submanifolds, and concludes by applying these results to the life and death of stars. Numerous examples and accompanying remarks make this an ideal textbook..

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Mathematical Horizons for Quantum Physics | ,

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Local Quantum Physics | Rudolf Haag

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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..

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Hilbert Space Operators in Quantum Physics | Jirí Blank,Pavel Exner,Miloslav Havlícek

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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..

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Mathematical Results in Quantum Physics | Pavel Exner

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The volume collects papers from talks given at QMath11 — Mathematical Results in Quantum Physics, which was held in Hradec Králové, September 2010. These papers bring new and interesting results in quantum mechanics and information, quantum field theory, random systems, quantum chaos, as well as in the physics of social systems. Part of the contribution is dedicated to Ari Laptev on the occasion of his 60th birthday, in recognition of his mathematical results and his service to the community. The QMath conference series has played an important role in mathematical physics for more than two decades, typically attracting many of the best results achieved in the last three-year period, and the meeting in Hradec Králové was no exception. Contents:Relative Entropies and Entanglement Monotones (Nilanjana Datta)Interacting Electrons on the Honeycomb Lattice (Alessandro Giuliani)Convergence Results for Thick Graphs (Olaf Post)Spectral Properties of Wigner Matrices (Benjamin Schlein)Semiclassical Spectral Bounds and Beyond (Timo Weidl)Spectral Problems in Spaces of Constant Curvature (Rafael D Benguria)Localization in Random Displacement Model (Michael Loss & Günther Stolz)Diffusion in Hamiltonian Quantum Systems (Wojciech De Roeck)Quantized Open Chaotic Systems (Stéphen Nonnenmacher)Reliability Issues in the Microscopic Modeling of Pedestrian Movement (Bernhard Steffen, Armin Seyfried & Maik Boltes)and other papers Readership: Graduate students, professionals and researchers in mathematical physics, quantum mechanics and field theory, quantum information, quantum chaos and physics of social systems. Keywords:Quantum Physics;Quantum Mechanics;Quantum Field Theory;Quantum Chaos;Quantum Information;Sociophysics.

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Quantum Mechanics for Mathematicians | Leon Armenovich Takhtadzhi͡an

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This book provides a comprehensive treatment of quantum mechanics from a mathematics perspective and is accessible to mathematicians starting with second-year graduate students. It addition to traditional topics, like classical mechanics, mathematical foundations of quantum mechanics, quantization, and the Schrodinger equation, this book gives a mathematical treatment of systems of identical particles with spin, and it introduces the reader to functional methods in quantum mechanics. This includes the Feynman path integral approach to quantum mechanics, integration in functional spaces, the relation between Feynman and Wiener integrals, Gaussian integration and regularized determinants of differential operators, fermion systems and integration over anticommuting (Grassmann) variables, supersymmetry and localization in loop spaces, and supersymmetric derivation of the Atiyah-Singer formula for the index of the Dirac operator. Prior to this book, mathematicians could find these topics only in physics textbooks and in specialized literature. This book is written in a concise style with careful attention to precise mathematics formulation of methods and results.Numerous problems, from routine to advanced, help the reader to master the subject. In addition to providing a fundamental knowledge of quantum mechanics, this book could also serve as a bridge for studying more advanced topics in quantum physics, among them quantum field theory. Prerequisites include standard first-year graduate courses covering linear and abstract algebra, topology and geometry, and real and complex analysis..

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A Course in Mathematical Physics | Walter Thirring

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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..

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General Principles of Quantum Field Theory | N.N. Bogolubov,Anatoly A. Logunov,A.I. Oksak,I. Todorov

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General Principles of Quantum Field Theory - N.N. Bogolubov,Anatoly A. Logunov,A.I. Oksak,I. Todorov Preview:

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..

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Mathematical Physics of Quantum Wires and Devices | N.E. Hurt

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This monograph on quantum wires and quantum devices is a companion vol ume to the author's Quantum Chaos and Mesoscopic Systems (Kluwer, Dordrecht, 1997). The goal of this work is to present to the reader the mathematical physics which has arisen in the study of these systems. The course which I have taken in this volume is to juxtapose the current work on the mathematical physics of quantum devices and the details behind the work so that the reader can gain an understanding of the physics, and where possible the open problems which re main in the development of a complete mathematical description of the devices. I have attempted to include sufficient background and references so that the reader can understand the limitations of the current methods and have direction to the original material for the research on the physics of these devices. As in the earlier volume, the monograph is a panoramic survey of the mathe matical physics of quantum wires and devices. Detailed proofs are kept to a min imum, with outlines of the principal steps and references to the primary sources as required. The survey is very broad to give a general development to a variety of problems in quantum devices, not a specialty volume..

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Topics in Quantum Mechanics | Floyd Williams

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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..

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Relativistic Quantum Mechanics | Hartmut Pilkuhn

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Relativistic Quantum Mechanics - Hartmut Pilkuhn Preview:

In this book, quantum mechanics is developed from the outset on a relativistic basis, using the superposition principle, Lorentz invariance and gauge invariance. Nonrelativistic quantum mechanics appears as a special case, and classical relativistic mechanics as another one. These special cases are important for giving plausible names to operators, for example "orbital angular momentum", "spin" or "magnetic moment". A subject which is treated for the first time in this book is the theory of binaries in terms of differential equations which have the mathematical structure of the corresponding one-body equations (Klein--Gordon for two spin- less particles, Dirac for two spinor particles)..

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Mathematical Concepts of Quantum Mechanics | Stephen J. Gustafson,Israel Michael Sigal

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Mathematical Concepts of Quantum Mechanics - Stephen J. Gustafson,Israel Michael Sigal Preview:

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.

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Quantum Information Processing with Finite Resources | Marco Tomamichel

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Quantum Information Processing with Finite Resources - Marco Tomamichel Preview:

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..

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Quantum Theory for Mathematicians | Brian C. Hall

Quantum Theory for Mathematicians Pdf/ePub eBook Quantum Theory for Mathematicians Pdf ebook download. Number Downloads: 1987 | Ebook Reads: 1987 | File: Quantum Theory for Mathematicians.pdf/epub | ISBNCode: 1461471168

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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..