Ground States Of Quantum Field Models
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Ground States Of Quantum Field Models
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Author : Fumio Hiroshima
language : en
Publisher: Springer
Release Date : 2019-08-16
Ground States Of Quantum Field Models written by Fumio Hiroshima and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-08-16 with Science categories.
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.
Existence Of Ground States For Infrared Critical Models Of Quantum Field Theory
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Author : Benjamin Hinrichs
language : de
Publisher:
Release Date : 2022*
Existence Of Ground States For Infrared Critical Models Of Quantum Field Theory written by Benjamin Hinrichs and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022* with categories.
When considering models of nonrelativistic quantum mechanical particles interacting with a field of massless relativistic bosons, one encounters an infrared problem. Heuristically, this is due to the fact that small energy fluctuations can create an infinite number of low-energy bosons, which causes infrared-divergences. From a mathematical perspective, this leads to the expectation that such systems cannot have a ground state, i.e., a stationary state at the lowest possible energy. In this thesis, we study two types of infrared-critical models. In case of the translation-invariant Nelson model, which describes the interaction of a nonrelativistic spinless quantum mechanical particle linearly coupled to the boson field, we extend previous proofs for the absence of ground states at fixed total momentum to the ultraviolet-renormalized model. Along the way, we study the dependence of the renormalized operators on the total momentum. Especially, we prove that in the physical case the domains of the renormalized operators with different total momentum have only the trivial vector space as intersection. The second model we study is the spin boson model. It describes a two-state quantum mechanical system, called spin, again linearly coupled to a boson field. It was previously proven by perturbative methods that the model has a ground state even in the physical infrared-critical case. This is attributed to a cancellation of divergences due to an underlying symmetry of the model. We provide a new non-perturbative proof for this fact, which allows us to extend the result to more singular models. Further, we can give an explicit coupling constant, below which the ground state exists. It is conjectured that there exists a critical coupling constant, above which the ground state ceases to exist.
Structural Aspects Of Quantum Field Theory In 2 Volumes
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Author : Gerhard Grensing
language : en
Publisher: World Scientific
Release Date : 2013-05-21
Structural Aspects Of Quantum Field Theory In 2 Volumes written by Gerhard Grensing and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-05-21 with Science categories.
'The book is primarily addressed to physicists. Nevertheless, as numerous examples are known in which exploration of the land where physics and mathematics overlap (and which quantum field theory definitely belongs to) resulted in important developments in mathematics, many mathematicians may also find this book interesting and even inspiring.'MathSciNetThis book is devoted to the subject of quantum field theory. It is divided into two volumes. The first can serve as a textbook on the 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 first volume is directed at graduate students who want to learn the basic facts about quantum field theory. It begins with a gentle introduction to classical field theory, including the standard model of particle physics, general relativity, and also supergravity. The transition to quantized fields is performed with path integral techniques, by means of which the one-loop renormalization of a self-interacting scalar quantum field, of quantum electrodynamics, and the asymptotic freedom of quantum chromodynamics is treated. In the last part of the first volume, the application of path integral methods to systems of quantum statistical mechanics is covered. The book ends with a rather detailed investigation of the fractional quantum Hall effect, and gives a stringent derivation of Laughlin's trial ground state wave function as an exact ground state.The second volume covers more advanced themes. In particular Connes' noncommutative geometry is dealt with in some considerable detail; the presentation attempts to acquaint the physics community with the substantial achievements that have been reached by means of this approach towards the understanding of the elusive Higgs particle. The book also covers the subject of quantum groups and its application to the fractional quantum Hall effect, as it is for this paradigmatic physical system that noncommutative geometry and quantum groups can be brought together.
Quantum Electrodynamics Of Strong Fields
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Author : Walter Greiner
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Quantum Electrodynamics Of Strong Fields written by Walter Greiner and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Science categories.
The fundamental goal of physics is an understanding of the forces of nature in their simplest and most general terms. Yet there is much more involved than just a basic set of equations which eventually has to be solved when applied to specific problems. We have learned in recent years that the structure of the ground state of field theories (with which we are generally concerned) plays an equally funda mental role as the equations of motion themselves. Heisenberg was probably the first to recognize that the ground state, the vacuum, could acquire certain prop erties (quantum numbers) when he devised a theory of ferromagnetism. Since then, many more such examples are known in solid state physics, e. g. supercon ductivity, superfluidity, in fact all problems concerned with phase transitions of many-body systems, which are often summarized under the name synergetics. Inspired by the experimental observation that also fundamental symmetries, such as parity or chiral symmetry, may be violated in nature, it has become wide ly accepted that the same field theory may be based on different vacua. Practical ly all these different field phases have the status of more or less hypothetical models, not (yet) directly accessible to experiments. There is one magnificent ex ception and this is the change of the ground state (vacuum) of the electron-posi tron field in superstrong electric fields.
Large Order Behaviour Of Perturbation Theory
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Author : J.C. Le Guillou
language : en
Publisher: Elsevier
Release Date : 2012-12-02
Large Order Behaviour Of Perturbation Theory written by J.C. Le Guillou and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-02 with Mathematics categories.
This volume is concerned with the determination of the behaviour of perturbation theory at large orders in quantum mechanics and quantum field theory, and its application to the problem of summation of perturbation series. Perturbation series in quantum field theory and in many quantum mechanics models are only asymptotic and thus diverge for all values of the expansion parameter. Their behaviour at large orders provides information about whether they define the theory uniquely (the problem of Borel summability). It suggests methods to extract numerical information from the series when the expansion parameter is not small. The articles reprinted here deal with the explicit evaluation of large-order behaviour in many quantum mechanics and field theory models. The large-order behaviour is related to barrier penetration effects for unphysical values of the expansion parameter, which can be calculated by WKB or instanton methods. The calculation of critical exponents of &fgr;4 field theory is presented as a practical application.
Beautiful Models
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Author : Bill Sutherland
language : en
Publisher: World Scientific Publishing Company
Release Date : 2004-06-21
Beautiful Models written by Bill Sutherland and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-06-21 with Science categories.
This invaluable book provides a broad introduction to the fascinating and beautiful subject of many-body quantum systems that can be solved exactly. The subject began with Bethe's famous solution of the one-dimensional Heisenberg magnet more than 70 years ago, soon after the invention of quantum mechanics. Since then, the diversity and scope of such systems have been steadily growing. Beautiful Models is self-contained and unified in presentation. It may be used as an advanced textbook by graduate students and even ambitious undergraduates in physics. It is also suitable for the non-experts in physics who wish to have an overview of some of the classic and fundamental models in the subject. The explanations in the book are detailed enough to capture the interest of the curious reader, and complete enough to provide the necessary background material needed to go further into the subject and explore the research literature.
Applications Of Statistical And Field Theory Methods To Condensed Matter
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Author : Dionys Baeriswyl
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Applications Of Statistical And Field Theory Methods To Condensed Matter written by Dionys Baeriswyl and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Science categories.
There is no doubt that we have, during the last decade, moved into a "golden age" of condensed matter science. The sequence of discoveries of novel new states of matter and their rapid assimilation into experimental and theoretical research, as well as devices, has been remarkable. To name but a few: spin glasses; incommensurate, fractal, quasicrystal structures; synthetic metals; quantum well fabrication; fractional quantum Hall effect: solid state chaos; heavy fermions; and most spectacularly high-temperature superconductivity. This rapid evolution has been marked by the need to address the reality of materials in "extreme" conditions - - disordered, nonlinear systems in reduced dimensions, restricted geometries and at mesoscopic scales, often with striking competitions between several length and frequency scales, and between strong electron-phonon and electron-electron interactions. In such new territory it is not surprising that very interdisciplinary approaches are being explored and traditional boundaries between subjects and disciplines re-defined. In theory, this is evident, for instance, in attempts: (1) to advance the state of the art for elec tronic structure calculations so as to handle strongly interacting many-body systems and delicate competitions for collective ground states (spin models or many-electron Hamiltoni ans, field theory, band structure, quantum chemistry and numerical approaches); or (2) to understand pattern formation and complex (including chaotic) dynamics in extended sys tems. This demands close involvement with applied mathematics, numerical simulations and statistical mechanics techniques.
Quantum Field Theory Under The Influence Of External Conditions
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Author : Michael Bordag
language : de
Publisher: Vieweg+Teubner Verlag
Release Date : 2013-11-13
Quantum Field Theory Under The Influence Of External Conditions written by Michael Bordag and has been published by Vieweg+Teubner Verlag this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-13 with Technology & Engineering categories.
This volume contains papers based on talks delivered at the Third Workshop on Quantum Field Theory under the /nftuence of External Conditions held at the University of Leipzig from September 18th to September 22nd, 1995. This series of Workshops is organized by the quantum field theory group at the University of Leipzig. The first and the second Workshop in the row have been held in 1989 and 1992. The present meeting has been joined by more than 70 participants. This fact underlines the vivid interest in the field covered by the Workshop ranging from the Casimir effect to semiclassical gravity. The material of this volume is organized along five subjects. The first part is devoted to the Casimir effect itself. The actual interest is mostly in non-stationary boundaries and a possible explanation of the phenomenon of sonoluminescence - a still open and challenging question. The second part deals with QED and QCD in external fields. The main interest was focused on the effective action approach, on some aspects of the bag model and on quantum effects in a conical background. The ground state in external fields is studied in the contributions of the third part. They demonstrate that the zeta function regularization tagether with the heat kerne! expansion is the most powerful method at present. New calculations of functional determinants, of finite temperature effects and an interesting method applicable in the presence of smooth background fields are presented.
Quantum Theory Of The Third Kind
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Author : Stephen Blaha
language : en
Publisher: Pingree-Hill Publishing
Release Date : 2005
Quantum Theory Of The Third Kind written by Stephen Blaha and has been published by Pingree-Hill Publishing this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with Mathematics categories.
This groundbreaking book develops a new form of quantum theory. First there was quantum mechanics. Then there was quantum field theory. Now we have quantum theory of the third kind: a new form of quantum field theory with quantum coordinates in the imaginary part of a complex space-time. This book is the second edition of ?A Finite Unified Quantum Field Theory of the Elementary Particle Standard Model and Quantum Gravity? with major additions on unitarity, relativistic invariance and the nature of space-time. Some major new results in this books are: A Unified Theory of QED, Weak Interactions, Strong Interactions and Quantum Gravity; A General Formulation of Divergence-free Quantum Field Theories (Detailed discussions of unitarity and special relativity showing these theories are physically acceptable.). A divergence-free quantum field theory for massive vector bosons: No need for the Higgs mechanism. The "Low Energy" Limit of elementary particle sector of unified theory approximates the Standard Model (& QED) to extreme accuracy. It suggests possible doubly charged dilepton, and other exotic, resonances. The "Large Distance", classical limit of Quantum Gravity sector is General Relativity. It suggests no ultra-light Black Holes exist. Gravity is repulsive (anti-gravity) at ultra-short distances. Two-tier gravity ?saves? the concept of a space-time point by evading Wigner?s classic argument against it. Based on experimental data a preferred local reference frame defined by Cosmic Background Radiation is shown to exist in each locale. (Preferred local inertial frames are used in two-tier quantum gravity whose dynamical equations are invariant under general relativistic transformations but whose ?ground state? breaks the invariance down to invariance under special relativity.) A New form of hidden dimensions is defined ? Quantum Dimensions ? dimensions implemented via a quantum gauge field. A New method in the Calculus of Variations ? composition of extrema ? is described.
Boulevard Of Broken Symmetries
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Author : Adriaan M. J. Schakel
language : en
Publisher: World Scientific
Release Date : 2008
Boulevard Of Broken Symmetries written by Adriaan M. J. Schakel and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Science categories.
This textbook covers the main topics in contemporary condensed matter physics in a modern and unified way, using quantum field theory in the functional-integral approach. The book highlights symmetry aspects in acknowledging that much of the collective behaviors of condensed matter systems at low temperatures emerge above a nontrivial ground state, which spontaneously breaks the symmetry.The emphasis is on effective field theories which provide an efficient and powerful description that is valid at long wavelengths and low frequencies. In conjunction with the emphasis on effective theories, a modern approach towards renormalization is taken, whereby a wavenumber cut-off is introduced to set a scale beyond which the microscopic model under consideration ceases to be valid. The unique and innovative character of this presentation, free of historical constraints, allows for a compact and self-contained treatment of the main topics in contemporary condensed matter physics.