Existence Of Ground States For Infrared Critical Models Of Quantum Field Theory
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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.
Analysis And Operator Theory
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Author : Themistocles M. Rassias
language : en
Publisher: Springer
Release Date : 2019-05-31
Analysis And Operator Theory written by Themistocles M. Rassias and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-05-31 with Mathematics categories.
Dedicated to Tosio Kato’s 100th birthday, this book contains research and survey papers on a broad spectrum of methods, theories, and problems in mathematics and mathematical physics. Survey papers and in-depth technical papers emphasize linear and nonlinear analysis, operator theory, partial differential equations, and functional analysis including nonlinear evolution equations, the Korteweg–de Vries equation, the Navier–Stokes equation, and perturbation theory of linear operators. The Kato inequality, the Kato type matrix limit theorem, the Howland–Kato commutator problem, the Kato-class of potentials, and the Trotter–Kato product formulae are discussed and analyzed. Graduate students, research mathematicians, and applied scientists will find that this book provides comprehensive insight into the significance of Tosio Kato’s impact to research in analysis and operator theory.
Analysis On Fock Spaces And Mathematical Theory Of Quantum Fields An Introduction To Mathematical Analysis Of Quantum Fields
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Author : Arai Asao
language : en
Publisher: World Scientific
Release Date : 2017-12-20
Analysis On Fock Spaces And Mathematical Theory Of Quantum Fields An Introduction To Mathematical Analysis Of Quantum Fields written by Arai Asao and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-12-20 with Science categories.
This book provides a comprehensive introduction to Fock space theory and its applications to mathematical quantum field theory. The first half of the book, Part I, is devoted to detailed descriptions of analysis on abstract Fock spaces (full Fock space, boson Fock space, fermion Fock space and boson-fermion Fock space). It includes the mathematics of second quantization, representation theory of canonical commutation relations and canonical anti-commutation relations, Bogoliubov transformations, infinite-dimensional Dirac operators and supersymmetric quantum field in an abstract form. The second half of the book, Part II, covers applications of the mathematical theories in Part I to quantum field theory. Four kinds of free quantum fields are constructed and detailed analyses are made. A simple interacting quantum field model, called the van Hove model, is fully analyzed in an abstract form. Moreover, a list of interacting quantum field models is presented and a short description to each model is given. To graduate students in mathematics or physics who are interested in the mathematical aspects of quantum field theory, this book is a good introductory text. It is also well suited for self-study and will provide readers a firm foundation of knowledge and mathematical techniques for reading more advanced books and current research articles in the field of mathematical analysis on quantum fields. Also, numerous problems are added to aid readers to develop a deeper understanding of the field. Contents: Linear Operators on Hilbert SpaceTensor Product of Hilbert SpacesTensor Product of Linear Operators on Hilbert SpacesFull Fock SpaceBoson Fock SpaceFermion Fock SpaceBoson-Fermion Fock SpaceTheory of Infinite-Dimensional Dirac Operators and Abstract Supersymmetric Quantum Fields General Theory of Quantum FieldsQuantum de Broglie FieldQuantum Klein–Gordon FieldQuantum Radiation FieldQuantum Dirac Fieldvan Hove ModelOverview of Interacting Quantum Field Models Readership: Advanced undergraduate and graduate students in mathematics or physics, mathematicians and mathematical physicists. Keywords: Fock Space;Second Quantization;Canonical Commutation Relation;Canonical Anti-Commutation Relation;Quantum Field;Bose Field;Fermi Field;Dirac Operator;Supersymmetry;Supersymmetric Quantum Field; Quantum Electrodynamics;van Hove ModelReview: Key Features: Detailed description of the theory of Fock spaces including full Fock spaces, boson Fock spaces, fermion Fock spaces and boson-fermion Fock spacesNew topics are included, such as the theory of infinite dimensional Dirac operators and an abstract supersymmetric quantum field theory, which have been originally developed by the authorDetailed treatment of mathematical constructions of free quantum field models as well as a simple interacting model
Quantum Field Theory And Statistical Mechanics
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Author : James Glimm
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Quantum Field Theory And Statistical Mechanics written by James Glimm 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.
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.
Collected Papers Vol 1 Quantum Field Theory And Statistical Mechanics
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Author : James Glimm
language : en
Publisher: Springer Science & Business Media
Release Date : 1985-01-01
Collected Papers Vol 1 Quantum Field Theory And Statistical Mechanics written by James Glimm 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 1985-01-01 with Science categories.
Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 325 Critical point dominance in quantum field models. . . . . . . . . . . . . . . . . . . . 326 q>,' quantum field model in the single-phase regions: Differentiability of the mass and bounds on critical exponents. . . . 341 Remark on the existence of q>:. . . • . . . . • . . . . • . . . . . . . . • . • . . . . . . . . . . • . 345 On the approach to the critical point . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 348 Critical exponents and elementary particles. . . . . . . . . . . . . . . . . . . . . . . . . . 362 V Particle Structure Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 371 Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 371 The entropy principle for vertex functions in quantum field models. . . . . 372 Three-particle structure of q>4 interactions and the scaling limit . . . . . . . . . 397 Two and three body equations in quantum field models. . . . . . . . . . . . . . . 409 Particles and scaling for lattice fields and Ising models. . . . . . . . . . . . . . . . 437 The resummation of one particle lines. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 450 VI Bounds on Coupling Constants Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 479 Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 479 Absolute bounds on vertices and couplings. . . . . . . . . . . . . . . . . . . . . . . . . . 480 The coupling constant in a q>4 field theory. . . . . . . . . . . . . . . . . . . . . . . . . . . 491 VII Confinement and Instantons Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 497 Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 497 Instantons in a U(I) lattice gauge theory: A coulomb dipole gas. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 498 Charges, vortices and confinement. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 516 ix VIII Reflection Positivity Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 531 Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 531 A note on reflection positivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 532 x Introduction 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.
Applications In Rigorous Quantum Field Theory
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Author : Fumio Hiroshima
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2020-03-09
Applications In Rigorous Quantum Field Theory written by Fumio Hiroshima and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-03-09 with Mathematics categories.
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.
Renormalization Group
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Author : Giuseppe Benfatto
language : en
Publisher: Princeton University Press
Release Date : 2020-11-10
Renormalization Group written by Giuseppe Benfatto and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-11-10 with Science categories.
Scaling and self-similarity ideas and methods in theoretical physics have, in the last twenty-five years, coalesced into renormalization-group methods. This book analyzes, from a single perspective, some of the most important applications: the critical-point theory in classical statistical mechanics, the scalar quantum field theories in two and three space-time dimensions, and Tomonaga's theory of the ground state of one-dimensional Fermi systems. The dimension dependence is discussed together with the related existence of anomalies (in Tomonaga's theory and in 4 -e dimensions for the critical point). The theory of Bose condensation at zero temperature in three space dimensions is also considered. Attention is focused on results that can in principle be formally established from a mathematical point of view. The 4 -e dimensions theory, Bose condensation, as well as a few other statements are exceptions to this rule, because no complete treatment is yet available. However, the truly mathematical details are intentionally omitted and only referred to. This is done with the purpose of stressing the unifying conceptual structure rather than the technical differences or subtleties.
Quantum Infrared Physics
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Author : H. M. Fried
language : en
Publisher: World Scientific Publishing Company
Release Date : 1995
Quantum Infrared Physics written by H. M. Fried 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 1995 with categories.
The common thread of the contributions collected here is an infrared approach to pressing problems in quantum field theory. Both high and low energy physics are represented, with much emphasis on QCD (Gribov horizons, infrared models, semiclassical applications, and effective Lagrangians). Other fields of interest are thermal infrared singularities, soft Pomeron physics, eikonal scattering phenomenology and the physics of bound states.
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.
An Introduction To Quantum Field Theory
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Author : Michael E. Peskin
language : en
Publisher: CRC Press
Release Date : 2018-05-04
An Introduction To Quantum Field Theory written by Michael E. Peskin and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-05-04 with Science categories.
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.