Perhaps due to its technical complexity, oftentimes one sees in research papers on nonequilibrium quantum field theory (NEqQFT) more emphasis placed on the field-theoretical formalisms than the ideas these sophisticated techniques attempt to capture, or the issues such problems embody. All the more so, we need some basic understanding of the important issues and concepts in nonequilibrium statistical mechanics (NEqSM), and how they are manifested in the context of quantum field theory. Many important advances in this field came from asking such questions and finding out how to answer them in the language of quantum field theory. Because of this somewhat skewed existing emphasis in NEqQFT, and since we do not assume the reader to have had a formal course on NEqSM before, we shall give a brief summary of the basic concepts of NEqSM relevant to the field-theoretical processes discussed in this book. Many fine monographs and reviews written on this subject take a more formal mathematical approach. approach. Since our purpose here is to familiarize readers with these issues and their subtleties, rather than training them to work in the rich field of NEqSM (which includes in addition to the traditional subject matter such as the projection operator formalism and open system concepts, also current topics at their foundation, such as dynamical systems and quantum chaos), we choose to approach these topics in a more intuitive and physical way, sacrificing by necessity rigor and completeness.
Perhaps due to its technical complexity, oftentimes one sees in research papers on nonequilibrium quantum field theory (NEqQFT) more emphasis placed on the field-theoretical formalisms than the ideas these sophisticated techniques attempt to capture, or the issues such problems embody. All the more so, we need some basic understanding of the important issues and concepts in nonequilibrium statistical mechanics (NEqSM), and how they are manifested in the context of quantum field theory. Many important advances in this field came from asking such questions and finding out how to answer them in the language of quantum field theory. Because of this somewhat skewed existing emphasis in NEqQFT, and since we do not assume the reader to have had a formal course on NEqSM before, we shall give a brief summary of the basic concepts of NEqSM relevant to the field-theoretical processes discussed in this book. Many fine monographs and reviews written on this subject take a more formal mathematical approach. approach. Since our purpose here is to familiarize readers with these issues and their subtleties, rather than training them to work in the rich field of NEqSM (which includes in addition to the traditional subject matter such as the projection operator formalism and open system concepts, also current topics at their foundation, such as dynamical systems and quantum chaos), we choose to approach these topics in a more intuitive and physical way, sacrificing by necessity rigor and completeness.
Bringing together the key ideas from nonequilibrium statistical mechanics and powerful methodology from quantum field theory, this book captures the essence of nonequilibrium quantum field theory. Beginning with the foundational aspects of the theory, the book presents important concepts and useful techniques, discusses issues of basic interest, and shows how thermal field, linear response, kinetic theories and hydrodynamics emerge. It also illustrates how these concepts and methodology are applied to current research topics including nonequilibrium phase transitions, thermalization in relativistic heavy ion collisions, the nonequilibrium dynamics of Bose-Einstein condensation, and the generation of structures from quantum fluctuations in the early Universe. Divided into five parts, with each part addressing a particular stage in the conceptual and technical development of the subject, this self-contained book is a valuable reference for graduate students and researchers in particle physics, gravitation, cosmology, atomic-optical and condensed matter physics.
The stated goal of this book is to fill a perceived gap between undergraduate texts on critical phenomena and advanced texts on quantum field theory, in the general area of renormalization methods. It is debatable whether this gap really exists nowadays, as a number of books have appeared in which it is made clear that field-theoretic renormalization group methods are not the preserve of particle theory, and indeed are far more easily appreciated in the contexts of statistical and condensed matter physics. Nevertheless, this volume does have a fresh aspect to it, perhaps because of the author's background in fluid dynamics and turbulence theory, rather than through the more traditional migration from particle physics. The book begins at a very elementary level, in an effort to motivate the use of renormalization methods. This is a worthy effort, but it is likely that most of this section will be thought too elementary by readers wanting to get their teeth into the subject, while those for whom this section is apparently written are likely to find the later chapters rather challenging. The author's particular approach then leads him to emphasise the role of renormalized perturbation theory (rather than the renormalization group) in a number of problems, including non-linear systems and turbulence. Some of these ideas will be novel and perhaps even surprising to traditionally trained field theorists. Most of the rest of the book is on far more familiar territory: the momentum-space renormalization group, epsilon-expansion, and so on. This is standard stuff, and, like many other textbooks, it takes a considerable chunk of the book to explain all the formalism. As a result, there is only space to discuss the standard ϕ 4 field theory as applied to the Ising model (even the N -vector model is not covered) so that no impression is conveyed of the power and extent of all the applications and generalizations of the techniques. It is regrettable that so much space is spent on rather oversimplified and unrelated models in the first part of the book that, in the end, the reader is left breathless on the threshold of the really interesting material. Despite the earlier emphasis on the application of renormalization ideas in dynamics, in the end the full power of the field-theoretical approach is not applied to the obvious arena of dynamic critical phenomena (where there certainly is currently a gap in the literature) but to the Navier--Stokes equations. The development of the book is somewhat illogical in places. Mean field theory interrupts discussion of block spin methods and scaling arguments---the two are distinct approaches. The Callan--Symanzik equation is introduced before Feynman diagrams are explained, so that there is a hiatus before the actual results for the critical exponents can be found. I think this book is too broad in some respects, and too limited in others, to be a really useful textbook for a course on renormalization methods. Those who have learned these ideas either from field theory, or from nonlinear systems, will find it more rewarding for the sections covering the topics with which they are less familiar. For this reason alone, the book should at least find a place on most library reference shelves.
The mathematical formalism of quantum theory in terms of vectors and operators in infinite-dimensional complex vector spaces is very abstract. The definitions of many mathematical quantities used do not seem to have an intuitive meaning, which makes it difficult to appreciate the mathematical formalism and understand quantum mechanics. This book provides intuition and motivation to the mathematics of quantum theory, introducing the mathematics in its simplest and familiar form, for instance, with three-dimensional vectors and operators, which can be readily understood. Feeling confident about and comfortable with the mathematics used helps readers appreciate and understand the concepts and formalism of quantum mechanics. This book is divided into four parts. Part I is a brief review of the general properties of classical and quantum systems. A general discussion of probability theory is also included which aims to help in understanding the probability theories relevant to quantum mechanics. Part II is a detailed study of the mathematics for quantum mechanics. Part III presents quantum mechanics in a series of postulates. Six groups of postulates are presented to describe orthodox quantum systems. Each statement of a postulate is supplemented with a detailed discussion. To make them easier to understand, the postulates for discrete observables are presented before those for continuous observables. Part IV presents several illustrative applications, which include harmonic and isotropic oscillators, charged particle in external magnetic fields and the Aharonov–Bohm effect. For easy reference, definitions, theorems, examples, comments, properties and results are labelled with section numbers. Various symbols and notations are adopted to distinguish different quantities explicitly and to avoid misrepresentation. Self-contained both mathematically and physically, the book is accessible to a wide readership, including astrophysicists, mathematicians and philosophers of science who are interested in the foundations of quantum mechanics.
This book presents the basic concepts and methods of quantum mechanics for upper level undergraduate students, allowing them to master its application to real physical situations. A postulate-based treatment is adopted together with a gradual development of the quantum formalism of wave functions, operators, measurement and temporal evolution. Standard topics of one-dimensional and atomic motion, angular momentum and approximation methods are presented in addition to detailed discussions of many-particle systems, atomic and nuclear radiation. Appropriate mathematical tools and techniques are provided wherever necessary. The core text is supplemented by 77 worked examples, some of which address more complex issues and aspects of present-day research. The aim is to make this textbook a realistic introduction to more advanced and specialized texts. The material provides full coverage of the subject matter, 94 problems with solutions and a further 93 with answers only
Including topics not traditionally covered in literature, such as (1+1)-dimensional QFT and classical 2D Coulomb gases, this book considers a wide range of models and demonstrates a number of situations to which they can be applied. Beginning with a treatise of nonrelativistic 1D continuum Fermi and Bose quantum gases of identical spinless particles, the book describes the quantum inverse scattering method and the analysis of the related Yang–Baxter equation and integrable quantum Heisenberg models. It also discusses systems within condensed matter physics, the complete solution of the sine-Gordon model and modern trends in the thermodynamic Bethe ansatz. Each chapter concludes with problems and solutions to help consolidate the reader's understanding of the theory and its applications. Basic knowledge of quantum mechanics and equilibrium statistical physics is assumed, making this book suitable for graduate students and researchers in statistical physics, quantum mechanics and mathematical and theoretical physics.
Preface Part I. Quantum Mechanics: 1. On the low density of Boson models: Langevin equation L. Accardi and L. Y. Gang 2. Schrodinger operators with potentials supported by null sets S. Albeverio, J. E. Fenstad, R. Hoegh-Krohn, W. Karwowski and T. Lindstrom 3. Landau Hamiltonians on symmetric spaces J. E. Avron and A. Pnueli 4. Renormalization group analysis and quasicrystals J. Bellissard 5. The measurement problem in the stochastic formulation of quantum mechanics Ph. Blanchard, M. Cini and M. Serva 6. Schrodinger operators at threshold D. Bolle 7. Spectral analysis and scattering theory for Schrodinger operators with an interaction supported by a regular curve J. F. Brasche and A. Teta 8. Lattice models of solids V. V. Evstratov and B. S. Pavlov 9. Schrodinger operators on unusual manifolds P. Exner and P. Seba 10. High energy resolvent estimates for Schrodinger operators A. Jensen 11. Point interactions as solvable models W. Kirsch 12. Stochastic model of quantum mechanics V. P. Maslov Part II. Quantum Field Theory: 13. Maximality of infinite dimensional Dirichlet forms and Hoegh-Krohn's model of quantum fields S. Albeverio and S. Kusuoka 14. Global Markov property in quantum field theory and statistical mechanics: a review on results and problems S. Albeverio and B. Zegarlinski 15. Hypercontractivity: a bibliographic review E. B. Davies, L. B. Gross and B. Simon 16. Progress and problems in algebraic quantum field theory S. Doplicher 17. Hoegh-Krohn's model of quantum fields and the absolute continuity of measures S. Kusuoka 18. Baryon states in lattice QCD R. A. Minlos and E. A. Zhinzhina 19. The energy of a Weyl soliton R. F. Streater Part III. Statistical Physics: 20. Morphology and classification of galaxies: a stochastic model S. Albeverio, Ph. Blanchard, D. Gandolfo, R. Hoegh-Krohn and M. Mebkhout 21. Thermodynamic inequalities for the surface tension and the geometry of the Wulff construction R. L. Dobrushin and S. B. Shlosman 22. Verification of the global Markov property for strongly coupled trigonometric interactions R. Gielerak 23. Decomposition of Ising models and the Mayer expansion C. M. Newman and G. A. Baker, Jr 24. Towards time-dynamics for bosonic systems in quantum statistical mechanics A. G. Shuhov, Yu. M. Suhov and A. V. Teslenko 25. Towards time-dynamics for bosonic systems in quantum statistical mechanics, 2 A. G. Shuhov and Yu. M. Suhov.