Download or read book Ground States of Quantum Field Models written by Fumio Hiroshima and published by Springer. This book was released on 2019-08-16 with total page 148 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides self-contained proofs of the existence of ground states of several interaction models in quantum field theory. Interaction models discussed here include the spin-boson model, the Nelson model with and without an ultraviolet cutoff, and the Pauli–Fierz model with and without dipole approximation in non-relativistic quantum electrodynamics. These models describe interactions between bose fields and quantum mechanical matters.A ground state is defined as the eigenvector associated with the bottom of the spectrum of a self-adjoint operator describing the Hamiltonian of a model. The bottom of the spectrum is however embedded in the continuum and then it is non-trivial to show the existence of ground states in non-perturbative ways. We show the existence of the ground state of the Pauli–Fierz mode, the Nelson model, and the spin-boson model, and several kinds of proofs of the existence of ground states are explicitly provided. Key ingredients are compact sets and compact operators in Hilbert spaces. For the Nelson model with an ultraviolet cutoff and the Pauli–Fierz model with dipole approximation we show not only the existence of ground states but also enhanced binding. The enhanced binding means that a system for zero-coupling has no ground state but it has a ground state after turning on an interaction.The book will be of interest to graduate students of mathematics as well as to students of the natural sciences who want to learn quantum field theory from a mathematical point of view. It begins with abstract compactness arguments in Hilbert spaces and definitions of fundamental facts of quantum field theory: boson Fock spaces, creation operators, annihilation operators, and second quantization. This book quickly takes the reader to a level where a wider-than-usual range of quantum field theory can be appreciated, and self-contained proofs of the existence of ground states and enhanced binding are presented.
Download or read book An Introduction To Quantum Field Theory written by Michael E. Peskin and published by CRC Press. This book was released on 2018-05-04 with total page 866 pages. Available in PDF, EPUB and Kindle. Book excerpt: An Introduction to Quantum Field Theory is a textbook intended for the graduate physics course covering relativistic quantum mechanics, quantum electrodynamics, and Feynman diagrams. The authors make these subjects accessible through carefully worked examples illustrating the technical aspects of the subject, and intuitive explanations of what is going on behind the mathematics. After presenting the basics of quantum electrodynamics, the authors discuss the theory of renormalization and its relation to statistical mechanics, and introduce the renormalization group. This discussion sets the stage for a discussion of the physical principles that underlie the fundamental interactions of elementary particle physics and their description by gauge field theories.
Download or read book Quantum Field Theory and the Standard Model written by Matthew D. Schwartz and published by Cambridge University Press. This book was released on 2014 with total page 869 pages. Available in PDF, EPUB and Kindle. Book excerpt: A modern introduction to quantum field theory for graduates, providing intuitive, physical explanations supported by real-world applications and homework problems.
Download or read book Quantum Field Theory in a Nutshell written by Anthony Zee and published by Princeton University Press. This book was released on 2010-02-01 with total page 605 pages. Available in PDF, EPUB and Kindle. Book excerpt: A fully updated edition of the classic text by acclaimed physicist A. Zee Since it was first published, Quantum Field Theory in a Nutshell has quickly established itself as the most accessible and comprehensive introduction to this profound and deeply fascinating area of theoretical physics. Now in this fully revised and expanded edition, A. Zee covers the latest advances while providing a solid conceptual foundation for students to build on, making this the most up-to-date and modern textbook on quantum field theory available. This expanded edition features several additional chapters, as well as an entirely new section describing recent developments in quantum field theory such as gravitational waves, the helicity spinor formalism, on-shell gluon scattering, recursion relations for amplitudes with complex momenta, and the hidden connection between Yang-Mills theory and Einstein gravity. Zee also provides added exercises, explanations, and examples, as well as detailed appendices, solutions to selected exercises, and suggestions for further reading. The most accessible and comprehensive introductory textbook available Features a fully revised, updated, and expanded text Covers the latest exciting advances in the field Includes new exercises Offers a one-of-a-kind resource for students and researchers Leading universities that have adopted this book include: Arizona State University Boston University Brandeis University Brown University California Institute of Technology Carnegie Mellon College of William & Mary Cornell Harvard University Massachusetts Institute of Technology Northwestern University Ohio State University Princeton University Purdue University - Main Campus Rensselaer Polytechnic Institute Rutgers University - New Brunswick Stanford University University of California - Berkeley University of Central Florida University of Chicago University of Michigan University of Montreal University of Notre Dame Vanderbilt University Virginia Tech University
Download or read book Quantum Field Theory and Statistical Mechanics written by James Glimm and published by Springer Science & Business Media. This book was released on 1985-01-01 with total page 430 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains a selection of expository articles on quantum field theory and statistical mechanics by James Glimm and Arthur Jaffe. They include a solution of the original interacting quantum field equations and a description of the physics which these equations contain. Quantum fields were proposed in the late 1920s as the natural framework which combines quantum theory with relativ ity. They have survived ever since. The mathematical description for quantum theory starts with a Hilbert space H of state vectors. Quantum fields are linear operators on this space, which satisfy nonlinear wave equations of fundamental physics, including coupled Dirac, Max well and Yang-Mills equations. The field operators are restricted to satisfy a "locality" requirement that they commute (or anti-commute in the case of fer mions) at space-like separated points. This condition is compatible with finite propagation speed, and hence with special relativity. Asymptotically, these fields converge for large time to linear fields describing free particles. Using these ideas a scattering theory had been developed, based on the existence of local quantum fields.
Download or read book Quantum Field Theory of Non equilibrium States written by Jørgen Rammer and published by Cambridge University Press. This book was released on 2011-03-03 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Quantum field theory is the application of quantum mechanics to systems with infinitely many degrees of freedom. This 2007 textbook presents quantum field theoretical applications to systems out of equilibrium. It introduces the real-time approach to non-equilibrium statistical mechanics and the quantum field theory of non-equilibrium states in general. It offers two ways of learning how to study non-equilibrium states of many-body systems: the mathematical canonical way and an easy intuitive way using Feynman diagrams. The latter provides an easy introduction to the powerful functional methods of field theory, and the use of Feynman diagrams to study classical stochastic dynamics is considered in detail. The developed real-time technique is applied to study numerous phenomena in many-body systems. Complete with numerous exercises to aid self-study, this textbook is suitable for graduate students in statistical mechanics and condensed matter physics.
Download or read book Methods of Quantum Field Theory in Statistical Physics written by Alekseĭ Alekseevich Abrikosov and published by . This book was released on 1963 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Quantum Field Theory written by Mark Srednicki and published by Cambridge University Press. This book was released on 2007-01-25 with total page 664 pages. Available in PDF, EPUB and Kindle. Book excerpt: Quantum field theory is the basic mathematical framework that is used to describe elementary particles. This textbook provides a complete and essential introduction to the subject. Assuming only an undergraduate knowledge of quantum mechanics and special relativity, this book is ideal for graduate students beginning the study of elementary particles. The step-by-step presentation begins with basic concepts illustrated by simple examples, and proceeds through historically important results to thorough treatments of modern topics such as the renormalization group, spinor-helicity methods for quark and gluon scattering, magnetic monopoles, instantons, supersymmetry, and the unification of forces. The book is written in a modular format, with each chapter as self-contained as possible, and with the necessary prerequisite material clearly identified. It is based on a year-long course given by the author and contains extensive problems, with password protected solutions available to lecturers at www.cambridge.org/9780521864497.
Download or read book Ground States of Quantum Field Models written by Fumio Hiroshima and published by . This book was released on 2019 with total page 148 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides self-contained proofs of the existence of ground states of several interaction models in quantum field theory. Interaction models discussed here include the spin-boson model, the Nelson model with and without an ultraviolet cutoff, and the Pauli-Fierz model with and without dipole approximation in non-relativistic quantum electrodynamics. These models describe interactions between bose fields and quantum mechanical matters. A ground state is defined as the eigenvector associated with the bottom of the spectrum of a self-adjoint operator describing the Hamiltonian of a model. The bottom of the spectrum is however embedded in the continuum and then it is non-trivial to show the existence of ground states in non-perturbative ways. We show the existence of the ground state of the Pauli-Fierz mode, the Nelson model, and the spin-boson model, and several kinds of proofs of the existence of ground states are explicitly provided. Key ingredients are compact sets and compact operators in Hilbert spaces. For the Nelson model with an ultraviolet cutoff and the Pauli-Fierz model with dipole approximation we show not only the existence of ground states but also enhanced binding. The enhanced binding means that a system for zero-coupling has no ground state but it has a ground state after turning on an interaction. The book will be of interest to graduate students of mathematics as well as to students of the natural sciences who want to learn quantum field theory from a mathematical point of view. It begins with abstract compactness arguments in Hilbert spaces and definitions of fundamental facts of quantum field theory: boson Fock spaces, creation operators, annihilation operators, and second quantization. This book quickly takes the reader to a level where a wider-than-usual range of quantum field theory can be appreciated, and self-contained proofs of the existence of ground states and enhanced binding are presented.
Download or read book Condensed Matter Field Theory written by Alexander Altland and published by Cambridge University Press. This book was released on 2010-03-11 with total page 785 pages. Available in PDF, EPUB and Kindle. Book excerpt: This primer is aimed at elevating graduate students of condensed matter theory to a level where they can engage in independent research. Topics covered include second quantisation, path and functional field integration, mean-field theory and collective phenomena.
Download or read book Structural Aspects Of Quantum Field Theory And Noncommutative Geometry Second Edition In 2 Volumes written by Gerhard Grensing and published by World Scientific. This book was released on 2021-07-15 with total page 1656 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book is devoted to the subject of quantum field theory. It is divided into two volumes. The first volume can serve as a textbook on main techniques and results of quantum field theory, while the second treats more recent developments, in particular the subject of quantum groups and noncommutative geometry, and their interrelation.The second edition is extended by additional material, mostly concerning the impact of noncommutative geometry on theories beyond the standard model of particle physics, especially the possible role of torsion in the context of the dark matter problem. Furthermore, the text includes a discussion of the Randall-Sundrum model and the Seiberg-Witten equations.
Download or read book Quantum Field Theory with Application to Quantum Nonlinear Optics written by Anatoli? Karolevich Prikarpatski? and published by World Scientific. This book was released on 2002 with total page 136 pages. Available in PDF, EPUB and Kindle. Book excerpt: Multi-photon excitation states of poly-atomic molecules undergoing a self-interaction via Kerr effect related processes are of great interest today. Their successful study must be both analytical and by means of modern quantum field theoretical tools. This book deals with these and related topics by developing modern quantum field theory methods for the analysis of radiative states in a nonlinear quantum-optical system. These lecture notes are ideally suited to graduate mathematical physics and physics students, but can also be of interest to mathematicians involved in applied physics problems, and physicists and chemists studying phenomena related with modern quantum-optical devices.
Download or read book Topics in the Theory of Schr dinger Operators written by Huzihiro Araki and published by World Scientific. This book was released on 2004 with total page 288 pages. Available in PDF, EPUB and Kindle. Book excerpt: This invaluable book presents reviews of some recent topics in the theory of Schrdinger operators. It includes a short introduction to the subject, a survey of the theory of the Schrdinger equation when the potential depends on the time periodically, an introduction to the so-called FBI transformation (also known as coherent state expansion) with application to the semi-classical limit of the S-matrix, an overview of inverse spectral and scattering problems, and a study of the ground state of the Pauli-Fierz model with the use of the functional integral. The material is accessible to graduate students and non-expert researchers.
Download or read book Applications in Rigorous Quantum Field Theory written by Fumio Hiroshima and published by Walter de Gruyter GmbH & Co KG. This book was released on 2020-03-09 with total page 558 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the second updated and extended edition of the successful book on Feynman-Kac theory. It offers a state-of-the-art mathematical account of functional integration methods in the context of self-adjoint operators and semigroups using the concepts and tools of modern stochastic analysis. In the second volume, these ideas are applied principally to a rigorous treatment of some fundamental models of quantum field theory.
Download or read book Foundations Of Quantum Field Theory written by Klaus D Rothe and published by World Scientific. This book was released on 2020-09-03 with total page 350 pages. Available in PDF, EPUB and Kindle. Book excerpt: Based on a two-semester course held at the University of Heidelberg, Germany, this book provides a solid basis for postgraduate students wishing to obtain a more profound understanding of the foundations of Quantum Field Theory. The book covers a wide spectrum of topics ranging from traditional operator and modern path integral methods, to different regularization and renormalization methods, asymptotic behavior of Green functions, a particular view on the Renormalization Group, and spontaneous symmetry breaking in effective potentials. Much effort has been made to present the material in a transparent, detailed and structured way, which should help the reader to follow the material.
Download or read book The Stability of Matter From Atoms to Stars written by Elliott H. Lieb and published by Springer Science & Business Media. This book was released on 2001-10-05 with total page 828 pages. Available in PDF, EPUB and Kindle. Book excerpt: Excellent current review of our knowledge of matter. In this new edition two new sections have been added: quantum electrodynamics and Boson systems.
Download or read book Stochastic Processes Physics and Geometry New Interplays II written by Sergio Albeverio and published by American Mathematical Soc.. This book was released on 2000 with total page 650 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume and Stochastic Processes, Physics and Geometry: New Interplays I present state-of-the-art research currently unfolding at the interface between mathematics and physics. Included are select articles from the international conference held in Leipzig (Germany) in honor of Sergio Albeverio's sixtieth birthday. The theme of the conference, "Infinite Dimensional (Stochastic) Analysis and Quantum Physics", was chosen to reflect Albeverio's wide-ranging scientific interests. The articles in these books reflect that broad range of interests and provide a detailed overview highlighting the deep interplay among stochastic processes, mathematical physics, and geometry. The contributions are written by internationally recognized experts in the fields of stochastic analysis, linear and nonlinear (deterministic and stochastic) PDEs, infinite dimensional analysis, functional analysis, commutative and noncommutative probability theory, integrable systems, quantum and statistical mechanics, geometric quantization, and neural networks. Also included are applications in biology and other areas. Most of the contributions are high-level research papers. However, there are also some overviews on topics of general interest. The articles selected for publication in these volumes were specifically chosen to introduce readers to advanced topics, to emphasize interdisciplinary connections, and to stress future research directions. Volume I contains contributions from invited speakers; Volume II contains additional contributed papers. Members of the Canadian Mathematical Society may order at the AMS member price.
