Analytic Aspects Of Quantum Fields

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Analytic Aspects Of Quantum Fields

Andrei A Bytsenko,Guido Cognola,Emilio Elizalde,Valter Moretti,Sergio Zerbini
Analytic Aspects Of Quantum Fields Book PDF

Author : Andrei A Bytsenko,Guido Cognola,Emilio Elizalde,Valter Moretti,Sergio Zerbini
Publisher : World Scientific
Page : 368 pages
File Size : 50,9 Mb
Release : 2003-10-14
Category : Science
ISBN : 9789814486033

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Analytic Aspects Of Quantum Fields by Andrei A Bytsenko,Guido Cognola,Emilio Elizalde,Valter Moretti,Sergio Zerbini Pdf

One of the aims of this book is to explain in a basic manner the seemingly difficult issues of mathematical structure using some specific examples as a guide. In each of the cases considered, a comprehensible physical problem is approached, to which the corresponding mathematical scheme is applied, its usefulness being duly demonstrated. The authors try to fill the gap that always exists between the physics of quantum field theories and the mathematical methods best suited for its formulation, which are increasingly demanding on the mathematical ability of the physicist.

Analytic Aspects of Quantum Fields

Andrei A. Bytsenko
Analytic Aspects of Quantum Fields Book PDF

Author : Andrei A. Bytsenko
Publisher : World Scientific
Page : 376 pages
File Size : 48,6 Mb
Release : 2003-01-01
Category : Science
ISBN : 9812775501

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Analytic Aspects of Quantum Fields by Andrei A. Bytsenko Pdf

One of the aims of this book is to explain in a basic manner the seemingly difficult issues of mathematical structure using some specific examples as a guide. In each of the cases considered, a comprehensible physical problem is approached, to which the corresponding mathematical scheme is applied, its usefulness being duly demonstrated. The authors try to fill the gap that always exists between the physics of quantum field theories and the mathematical methods best suited for its formulation, which are increasingly demanding on the mathematical ability of the physicist. Contents: Survey of Path Integral Quantization and Regularization Techniques; The Zeta-Function Regularization Method; Generalized Spectra and Spectral Functions on Non-Commutative Spaces; Spectral Functions of Laplace Operator on Locally Symmetric Spaces; Spinor Fields; Field Fluctuations and Related Variances; The Multiplicative Anomaly; Applications of the Multiplicative Anomaly; The Casimir Effect. Readership: Mathematical and high energy physicists.

Analysis On Fock Spaces And Mathematical Theory Of Quantum Fields: An Introduction To Mathematical Analysis Of Quantum Fields

Arai Asao
Analysis On Fock Spaces And Mathematical Theory Of Quantum Fields An Introduction To Mathematical Analysis Of Quantum Fields Book PDF

Author : Arai Asao
Publisher : World Scientific
Page : 892 pages
File Size : 43,7 Mb
Release : 2017-12-20
Category : Science
ISBN : 9789813207134

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Analysis On Fock Spaces And Mathematical Theory Of Quantum Fields: An Introduction To Mathematical Analysis Of Quantum Fields by Arai Asao Pdf

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

Aspects of Quantum Field Theory in Curved Spacetime

Stephen A. Fulling
Aspects of Quantum Field Theory in Curved Spacetime Book PDF

Author : Stephen A. Fulling
Publisher : Cambridge University Press
Page : 332 pages
File Size : 51,6 Mb
Release : 1989-08-24
Category : Mathematics
ISBN : 0521377684

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Aspects of Quantum Field Theory in Curved Spacetime by Stephen A. Fulling Pdf

The theory of quantum fields on curved spacetimes has attracted great attention since the discovery, by Stephen Hawking, of black-hole evaporation. It remains an important subject for the understanding of such contemporary topics as inflationary cosmology, quantum gravity and superstring theory. This book provides, for mathematicians, an introduction to this field of physics in a language and from a viewpoint which such a reader should find congenial. Physicists should also gain from reading this book a sound grasp of various aspects of the theory, some of which have not been particularly emphasised in the existing review literature. The topics covered include normal-mode expansions for a general elliptic operator, Fock space, the Casimir effect, the 'Klein' paradox, particle definition and particle creation in expanding universes, asymptotic expansion of Green's functions and heat kernels, and renormalisation of the stress tensor. The style is pedagogic rather than formal; some knowledge of general relativity and differential geometry is assumed, but the author does supply background material on functional analysis and quantum field theory as required. The book arose from a course taught to graduate students and could be used for self-study or for advanced courses in relativity and quantum field theory.

Ontological Aspects of Quantum Field Theory

Meinard Kuhlmann,Holger Lyre,Andrew Wayne
Ontological Aspects of Quantum Field Theory Book PDF

Author : Meinard Kuhlmann,Holger Lyre,Andrew Wayne
Publisher : World Scientific
Page : 376 pages
File Size : 51,7 Mb
Release : 2002-11-26
Category : Science
ISBN : 9789814487337

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Ontological Aspects of Quantum Field Theory by Meinard Kuhlmann,Holger Lyre,Andrew Wayne Pdf

Quantum field theory (QFT) provides the framework for many fundamental theories in modern physics, and over the last few years there has been growing interest in its historical and philosophical foundations. This anthology on the foundations of QFT brings together 15 essays by well-known researchers in physics, the philosophy of physics, and analytic philosophy. Many of these essays were first presented as papers at the conference “Ontological Aspects of Quantum Field Theory”, held at the Zentrum für interdisziplinäre Forschung (ZiF), Bielefeld, Germany. The essays contain cutting-edge work on ontological aspects of QFT, including: the role of measurement and experimental evidence, corpuscular versus field-theoretic interpretations of QFT, the interpretation of gauge symmetry, and localization. This book is ideally suited to anyone with an interest in the foundations of quantum physics, including physicists, philosophers and historians of physics, as well as general readers interested in philosophy or science. Contents:Approaches to Ontology:Candidate General Ontologies for Situating Quantum Field Theory (P Simons)‘Quanta’, Tropes, or Processes: Ontologies for QFT Beyond the Myth of Substance (J Seibt)Analytical Ontologists in Action: A Comment on Seibt and Simons (M Kuhlmann)How Do Field Theories Refer to Entities in a Field? (S Y Auyang)Field Ontologies for QFT:A Naive View of the Quantum Field (A Wayne)Comments on Paul Teller's Book, “An Interpretive Introduction to Quantum Field Theory” (G Fleming)So What Is the Quantum Field? (P Teller)Relativity, Measurement and Renormalization:On the Nature of Measurement Records in Relativistic Quantum Field Theory (J A Barrett)No Place for Particles in Relativistic Quantum Theories? (H Halvorson & R Clifton)Events and Covariance in the Interpretation of Quantum Field Theory (D Dieks)Measurement and Ontology: What Kind of Evidence Can We Have for Quantum Fields? (B Falkenburg)Renormalization and the Disunity of Science (N Huggett)Gauge Symmetries and the Vacuum:The Interpretation of Gauge Symmetry (M Redhead)Comment on Redhead: The Interpretation of Gauge Symmetry (M Drieschner et al.)Is the Zero-Point Energy Real? (S Saunders)Two Comments on the Vacuum in Algebraic Quantum Field Theory (M Rédei) Readership: Physicists, historians of physics and philosophers. Keywords:Quantum Field Theory;Ontology;Foundations of Physics;Philosophy;Measurement;Gauge Field TheoryReviews:“A strength of the volume is its inclusion of commentaries and exchanges.”Studies in History and Philosophy of Modern Physics

Non-perturbative Quantum Field Theory: Mathematical Aspects And Applications

Jurg Frohlich
Non perturbative Quantum Field Theory Mathematical Aspects And Applications Book PDF

Author : Jurg Frohlich
Publisher : World Scientific
Page : 854 pages
File Size : 48,9 Mb
Release : 1992-04-29
Category : Electronic
ISBN : 9789814506564

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Non-perturbative Quantum Field Theory: Mathematical Aspects And Applications by Jurg Frohlich Pdf

Compiled to illustrate the recent history of Quantum Field Theory and its trends, this collection of selected reprints by Jürg Fröhlich, a leading theoretician in the field, is a comprehensive guide of the more mathematical aspects of the subject. Results and methods of the past fifteen years are reviewed. The analytical methods employed are non-perturbative and, for the larger part, mathematically rigorous. Most articles are review articles surveying certain important developments in quantum field theory and guiding the reader towards the original literature.The volume begins with a comprehensive introduction by Jürg Fröhlich.The theory of phase transitions and continuous symmetry breaking is reviewed in the first section. The second section discusses the non-perturbative quantization of topological solitons. The third section is devoted to the study of gauge fields. A paper on the triviality of λϖ4 — theory in four and more dimensions is found in the fourth section, while the fifth contains two articles on “random geometry”. The sixth and final part addresses topics in low-dimensional quantum field theory, including braid statistics, two-dimensional conformal field theory and an application to condensed matter theory.

General Principles of Quantum Field Theory

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

Author : N.N. Bogolubov,Anatoly A. Logunov,A.I. Oksak,I. Todorov
Publisher : Springer Science & Business Media
Page : 714 pages
File Size : 45,9 Mb
Release : 2012-12-06
Category : Science
ISBN : 9789400904910

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

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.

Quantum and Non-Commutative Analysis

Huzihiro Araki,Keiichi R. Ito,Akitaka Kishimoto,Izumi Ojima
Quantum and Non Commutative Analysis Book PDF

Author : Huzihiro Araki,Keiichi R. Ito,Akitaka Kishimoto,Izumi Ojima
Publisher : Springer Science & Business Media
Page : 452 pages
File Size : 43,6 Mb
Release : 2013-04-17
Category : Science
ISBN : 9789401728232

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Quantum and Non-Commutative Analysis by Huzihiro Araki,Keiichi R. Ito,Akitaka Kishimoto,Izumi Ojima Pdf

In the past decade, there has been a sudden and vigorous development in a number of research areas in mathematics and mathematical physics, such as theory of operator algebras, knot theory, theory of manifolds, infinite dimensional Lie algebras and quantum groups (as a new topics), etc. on the side of mathematics, quantum field theory and statistical mechanics on the side of mathematical physics. The new development is characterized by very strong relations and interactions between different research areas which were hitherto considered as remotely related. Focussing on these new developments in mathematical physics and theory of operator algebras, the International Oji Seminar on Quantum Analysis was held at the Kansai Seminar House, Kyoto, JAPAN during June 25-29, 1992 by a generous sponsorship of the Japan Society for the Promotion of Science and the Fujihara Foundation of Science, as a workshop of relatively small number of (about 50) invited participants. This was followed by an open Symposium at RIMS, described below by its organizer, A. Kishimoto. The Oji Seminar began with two key-note addresses, one by V.F.R. Jones on Spin Models in Knot Theory and von Neumann Algebras and by A. Jaffe on Where Quantum Field Theory Has Led. Subsequently topics such as Subfactors and Sector Theory, Solvable Models of Statistical Mechanics, Quantum Field Theory, Quantum Groups, and Renormalization Group Ap proach, are discussed. Towards the end, a panel discussion on Where Should Quantum Analysis Go? was held.

Structural Aspects Of Quantum Field Theory And Noncommutative Geometry (Second Edition) (In 2 Volumes)

Gerhard Grensing
Structural Aspects Of Quantum Field Theory And Noncommutative Geometry Second Edition In 2 Volumes Book PDF

Author : Gerhard Grensing
Publisher : World Scientific
Page : 1656 pages
File Size : 43,7 Mb
Release : 2021-07-15
Category : Science
ISBN : 9789811237096

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Structural Aspects Of Quantum Field Theory And Noncommutative Geometry (Second Edition) (In 2 Volumes) by Gerhard Grensing Pdf

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.

Infinite-Dimensional Dirac Operators and Supersymmetric Quantum Fields

Asao Arai
Infinite Dimensional Dirac Operators and Supersymmetric Quantum Fields Book PDF

Author : Asao Arai
Publisher : Springer Nature
Page : 123 pages
File Size : 41,6 Mb
Release : 2022-10-18
Category : Science
ISBN : 9789811956782

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Infinite-Dimensional Dirac Operators and Supersymmetric Quantum Fields by Asao Arai Pdf

This book explains the mathematical structures of supersymmetric quantum field theory (SQFT) from the viewpoints of functional and infinite-dimensional analysis. The main mathematical objects are infinite-dimensional Dirac operators on the abstract Boson–Fermion Fock space. The target audience consists of graduate students and researchers who are interested in mathematical analysis of quantum fields, including supersymmetric ones, and infinite-dimensional analysis. The major topics are the clarification of general mathematical structures that some models in the SQFT have in common, and the mathematically rigorous analysis of them. The importance and the relevance of the subject are that in physics literature, supersymmetric quantum field models are only formally (heuristically) considered and hence may be ill-defined mathematically. From a mathematical point of view, however, they suggest new aspects related to infinite-dimensional geometry and analysis. Therefore, it is important to show the mathematical existence of such models first and then study them in detail. The book shows that the theory of the abstract Boson–Fermion Fock space serves this purpose. The analysis developed in the book also provides a good example of infinite-dimensional analysis from the functional analysis point of view, including a theory of infinite-dimensional Dirac operators and Laplacians.

Spectral Theory and Quantum Mechanics

Valter Moretti
Spectral Theory and Quantum Mechanics Book PDF

Author : Valter Moretti
Publisher : Springer
Page : 950 pages
File Size : 46,8 Mb
Release : 2018-01-30
Category : Mathematics
ISBN : 9783319707068

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Spectral Theory and Quantum Mechanics by Valter Moretti Pdf

This book discusses the mathematical foundations of quantum theories. It offers an introductory text on linear functional analysis with a focus on Hilbert spaces, highlighting the spectral theory features that are relevant in physics. After exploring physical phenomenology, it then turns its attention to the formal and logical aspects of the theory. Further, this Second Edition collects in one volume a number of useful rigorous results on the mathematical structure of quantum mechanics focusing in particular on von Neumann algebras, Superselection rules, the various notions of Quantum Symmetry and Symmetry Groups, and including a number of fundamental results on the algebraic formulation of quantum theories. Intended for Master's and PhD students, both in physics and mathematics, the material is designed to be self-contained: it includes a summary of point-set topology and abstract measure theory, together with an appendix on differential geometry. The book also benefits established researchers by organizing and presenting the profusion of advanced material disseminated in the literature. Most chapters are accompanied by exercises, many of which are solved explicitly."

Scattering in Quantum Field Theories

Daniel Iagolnitzer
Scattering in Quantum Field Theories Book PDF

Author : Daniel Iagolnitzer
Publisher : Princeton University Press
Page : 312 pages
File Size : 49,9 Mb
Release : 2014-07-14
Category : Science
ISBN : 9781400863167

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Scattering in Quantum Field Theories by Daniel Iagolnitzer Pdf

Axiomatic and constructive approaches to quantum field theory first aim to establish it on precise, non-perturbative bases: general axioms and rigorous definition of specific theories respectively. From the viewpoint of particle physics, the goal is then to develop a relativistic scattering theory, including particle analysis and the derivation of general properties of collision amplitudes. Taking into account successive improvements, this book provides a modern, self-contained, and coherent presentation of important developments from the last twenty years, most of which have not been treated or discussed in detail in earlier books. These developments include in particular the axiomatic derivation, in massive theories, of general causal and momentum-space analyticity properties of multiparticle collision amplitudes; the constructive definition, initially in the (unphysical) euclidean space, of various models including non-super-renormalizable theories treated in the 1980s via phase-space expansions; and the subsequent constructive approach to scattering theory, which provides information on the mass spectrum, asymptotic completeness, and multiparticle structure in increasingly higher energy regions. Originally published in 1993. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.

Spectral Theory and Quantum Mechanics

Valter Moretti
Spectral Theory and Quantum Mechanics Book PDF

Author : Valter Moretti
Publisher : Springer Science & Business Media
Page : 742 pages
File Size : 52,6 Mb
Release : 2013-04-02
Category : Mathematics
ISBN : 9788847028357

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Spectral Theory and Quantum Mechanics by Valter Moretti Pdf

This book pursues the accurate study of the mathematical foundations of Quantum Theories. It may be considered an introductory text on linear functional analysis with a focus on Hilbert spaces. Specific attention is given to spectral theory features that are relevant in physics. Having left the physical phenomenology in the background, it is the formal and logical aspects of the theory that are privileged. Another not lesser purpose is to collect in one place a number of useful rigorous statements on the mathematical structure of Quantum Mechanics, including some elementary, yet fundamental, results on the Algebraic Formulation of Quantum Theories. In the attempt to reach out to Master's or PhD students, both in physics and mathematics, the material is designed to be self-contained: it includes a summary of point-set topology and abstract measure theory, together with an appendix on differential geometry. The book should benefit established researchers to organise and present the profusion of advanced material disseminated in the literature. Most chapters are accompanied by exercises, many of which are solved explicitly.

Rigorous Quantum Field Theory

Anne Boutet de Monvel,Detlev Buchholz,Daniel Iagolnitzer,Ugo Moschella
Rigorous Quantum Field Theory Book PDF

Author : Anne Boutet de Monvel,Detlev Buchholz,Daniel Iagolnitzer,Ugo Moschella
Publisher : Springer Science & Business Media
Page : 326 pages
File Size : 54,5 Mb
Release : 2006-12-15
Category : Science
ISBN : 9783764374341

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Rigorous Quantum Field Theory by Anne Boutet de Monvel,Detlev Buchholz,Daniel Iagolnitzer,Ugo Moschella Pdf

Jacques Bros has greatly advanced our present understanding of rigorous quantum field theory through numerous contributions; this book arose from an international symposium held in honour of Bros on the occasion of his 70th birthday. Key topics in this volume include: Analytic structures of Quantum Field Theory (QFT), renormalization group methods, gauge QFT, stability properties and extension of the axiomatic framework, QFT on models of curved spacetimes, QFT on noncommutative Minkowski spacetime.

Introduction to Algebraic and Constructive Quantum Field Theory

John C. Baez,Irving E. Segal,Zhengfang Zhou
Introduction to Algebraic and Constructive Quantum Field Theory Book PDF

Author : John C. Baez,Irving E. Segal,Zhengfang Zhou
Publisher : Princeton University Press
Page : 310 pages
File Size : 48,7 Mb
Release : 2014-07-14
Category : Science
ISBN : 9781400862504

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Introduction to Algebraic and Constructive Quantum Field Theory by John C. Baez,Irving E. Segal,Zhengfang Zhou Pdf

The authors present a rigorous treatment of the first principles of the algebraic and analytic core of quantum field theory. Their aim is to correlate modern mathematical theory with the explanation of the observed process of particle production and of particle-wave duality that heuristic quantum field theory provides. Many topics are treated here in book form for the first time, from the origins of complex structures to the quantization of tachyons and domains of dependence for quantized wave equations. This work begins with a comprehensive analysis, in a universal format, of the structure and characterization of free fields, which is illustrated by applications to specific fields. Nonlinear local functions of both free fields (or Wick products) and interacting fields are established mathematically in a way that is consistent with the basic physical constraints and practice. Among other topics discussed are functional integration, Fourier transforms in Hilbert space, and implementability of canonical transformations. The authors address readers interested in fundamental mathematical physics and who have at least the training of an entering graduate student. A series of lexicons connects the mathematical development with the underlying physical motivation or interpretation. The examples and problems illustrate the theory and relate it to the scientific literature. Originally published in 1992. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.