Infinite Dimensional Dirac Operators And Supersymmetric Quantum Fields

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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 : 43,6 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.

Infinite-dimensional Dirac Operators and Supersymmetric Quantum Fields

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

Author : Asao Arai
Publisher : Unknown
Page : 0 pages
File Size : 40,7 Mb
Release : 2022
Category : Quantum field theory
ISBN : 8981195676

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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 BosonFermion 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 BosonFermion 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.

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 : 51,7 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

Recent Developments in Infinite-Dimensional Analysis and Quantum Probability

Luigi Accardi,Hui-Hsiung Kuo,Nobuaki Obata,Kimiaki Saito,Si Si,L. Streit
Recent Developments in Infinite Dimensional Analysis and Quantum Probability Book PDF

Author : Luigi Accardi,Hui-Hsiung Kuo,Nobuaki Obata,Kimiaki Saito,Si Si,L. Streit
Publisher : Springer Science & Business Media
Page : 455 pages
File Size : 54,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9789401008426

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Recent Developments in Infinite-Dimensional Analysis and Quantum Probability by Luigi Accardi,Hui-Hsiung Kuo,Nobuaki Obata,Kimiaki Saito,Si Si,L. Streit Pdf

Recent Developments in Infinite-Dimensional Analysis and Quantum Probability is dedicated to Professor Takeyuki Hida on the occasion of his 70th birthday. The book is more than a collection of articles. In fact, in it the reader will find a consistent editorial work, devoted to attempting to obtain a unitary picture from the different contributions and to give a comprehensive account of important recent developments in contemporary white noise analysis and some of its applications. For this reason, not only the latest results, but also motivations, explanations and connections with previous work have been included. The wealth of applications, from number theory to signal processing, from optimal filtering to information theory, from the statistics of stationary flows to quantum cable equations, show the power of white noise analysis as a tool. Beyond these, the authors emphasize its connections with practically all branches of contemporary probability, including stochastic geometry, the structure theory of stationary Gaussian processes, Neumann boundary value problems, and large deviations.

Nonperturbative Quantum Field Theory

G. Hooft,A. Jaffe,G. Mack,P.K. Mitter,R. Stora
Nonperturbative Quantum Field Theory Book PDF

Author : G. Hooft,A. Jaffe,G. Mack,P.K. Mitter,R. Stora
Publisher : Springer Science & Business Media
Page : 603 pages
File Size : 43,5 Mb
Release : 2012-12-06
Category : Science
ISBN : 9781461307297

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Nonperturbative Quantum Field Theory by G. Hooft,A. Jaffe,G. Mack,P.K. Mitter,R. Stora Pdf

During the past 15 years, quantum field theory and classical statistical mechanics have merged into a single field, and the need for nonperturbative methods for the description of critical phenomena in statistical mechanics as well as for problems in elementary particle physics are generally acknowledged. Such methods formed the central theme of the 1987 Cargese Advanced Study Institut. e on "Nonpert. urbat. ive Quantum Field Theory." The use of conformal symmet. ry has been of central interest in recent years, and was a main subject at. t. he ASI. Conformal invariant quantum field theory describes statistical mechanical systems exactly at a critical point, and can be analysed to a remarkable ext. ent. by group t. heoretical methods. Very strong results have been obtained for 2-dimensional systems. Conformal field theory is also the basis of string theory, which offers some hope of providing a unified t. heory of all interactions between elementary particles. Accordingly, a number of lectures and seminars were presented on these two topics. After syst. ematic introductory lectures, conformal field theory on Riemann surfaces, orbifolds, sigma models, and application of loop group theory and Grassmannians were discussed, and some ideas on modular geometry were presented. Other lectures combined' traditional techniques of constructive quant. um field theory with new methods such as the use of index-t. heorems and infinite dimensional (Kac Moody) symmetry groups. The problems encountered in a quantum mechanical description of black holes were discussed in detail.

Partial Differential Equations and Spectral Theory

Michael Demuth,Bert-Wolfgang Schulze
Partial Differential Equations and Spectral Theory Book PDF

Author : Michael Demuth,Bert-Wolfgang Schulze
Publisher : Birkhäuser
Page : 346 pages
File Size : 44,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783034882316

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Partial Differential Equations and Spectral Theory by Michael Demuth,Bert-Wolfgang Schulze Pdf

The intention of the international conference PDE2000 was to bring together specialists from different areas of modern analysis, mathematical physics and geometry, to discuss not only the recent progress in their own fields but also the interaction between these fields. The special topics of the conference were spectral and scattering theory, semiclassical and asymptotic analysis, pseudodifferential operators and their relation to geometry, as well as partial differential operators and their connection to stochastic analysis and to the theory of semigroups. The scientific advisory board of the conference in Clausthal consisted of M. Ben-Artzi (Jerusalem), Chen Hua (Peking), M. Demuth (Clausthal), T. Ichinose (Kanazawa), L. Rodino (Turin), B.-W. Schulze (Potsdam) and J. Sjöstrand (Paris). The book is aimed at researchers in mathematics and mathematical physics with interests in partial differential equations and all its related fields.

Constructive Quantum Field Theory II

G. Velo,A.S. Wightman
Constructive Quantum Field Theory II Book PDF

Author : G. Velo,A.S. Wightman
Publisher : Springer Science & Business Media
Page : 344 pages
File Size : 40,5 Mb
Release : 2012-12-06
Category : Science
ISBN : 9781468458381

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Constructive Quantum Field Theory II by G. Velo,A.S. Wightman Pdf

The seventh Ettore Majorana International School of Mathematical Physics was :Jeld at the Centro della Cultura Scientifica Erice. Sicily, 1-15 July 1988. The present volume collects lecture notes on the session which was entitled Con8tructive Quantum Field Theory lI. The II refers to the fact that the first such school in 1973 was devoted ,0 the same subject. The school was a NATO Advanced Study Institute sponsored Jy the Italian Ministry of Scientific and Technological Research and the Regional 3icilian Government. At the time of the 1973 Erice School on Constructive Field Theory, the speakers :ould summarize a decade of effort on the solution of superrenormalizable models in two dimensional space-time leading to the verification of the axioms of relativistic :J. uantum field theory for these examples. The resulting lecture notes have proved ,0 be exceptionally useful and are still in print. In the decade and a half that have ~lapsed since that time, there has been much hard work with the ultimate objective of providing a rigorous mathematical foundation for the quantum field theories in four iimensional space-time that summarize a large fraction of our current understanding )f elementary particle physics: QCD and the electroweak theory. The lecture notes )f the 1988 school record the fact that, although this objective has not been reached, Important progress has been made. The ultraviolet stability of Yang-Mills theory In four dimensions has been treated and renormalizable (not superrenormalizable) models in two dimensional space-time, Gross-Neveu models, have been solved.

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 : 48,5 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.

The Legacy of John Von Neumann

James G. Glimm,John Impagliazzo,Isadore Singer
The Legacy of John Von Neumann Book PDF

Author : James G. Glimm,John Impagliazzo,Isadore Singer
Publisher : American Mathematical Soc.
Page : 346 pages
File Size : 41,6 Mb
Release : 2006-09-08
Category : Mathematics
ISBN : 0821868160

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The Legacy of John Von Neumann by James G. Glimm,John Impagliazzo,Isadore Singer Pdf

The ideas of John von Neumann have had a profound influence on modern mathematics and science. One of the great thinkers of our century, von Neumann initiated major branches of mathematics--from operator algebras to game theory to scientific computing--and had a fundamental impact on such areas as self-adjoint operators, ergodic theory and the foundations of quantum mechanics, and numerical analysis and the design of the modern computer. This volume contains the proceedings of an AMS Symposium in Pure Mathematics, held at Hofstra University, in May 1988. The symposium brought together some of the foremost researchers in the wide range of areas in which von Neumann worked. These articles illustrate the sweep of von Neumann's ideas and thinking and document their influence on contemporary mathematics. In addition, some of those who knew von Neumann when he was alive have presented here personal reminiscences about him. This book is directed to those interested in operator theory, game theory, ergodic theory, and scientific computing, as well as to historians of mathematics and others having an interest in the contemporary history of the mathematical sciences. This book will give readers an appreciation for the workings of the mind of one of the mathematical giants of our time.

New Dualities of Supersymmetric Gauge Theories

Jörg Teschner
New Dualities of Supersymmetric Gauge Theories Book PDF

Author : Jörg Teschner
Publisher : Springer
Page : 467 pages
File Size : 48,5 Mb
Release : 2015-11-17
Category : Science
ISBN : 9783319187693

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New Dualities of Supersymmetric Gauge Theories by Jörg Teschner Pdf

This book reviews a number of spectacular advances that have been made in the study of supersymmetric quantum field theories in the last few years. Highlights include exact calculations of Wilson loop expectation values, and highly nontrivial quantitative checks of the long-standing electric-magnetic duality conjectures The book starts with an introductory article presenting a survey of recent advances, aimed at a wide audience with a background and interest in theoretical physics. The following articles are written for advanced students and researchers in quantum field theory, string theory and mathematical physics, our goal being to familiarize these readers with the forefront of current research. The topics covered include recent advances in the classification and vacuum structure of large families of N=2 supersymmetric field theories, followed by an extensive discussion of the localisation method, one of the most powerful tools for exact studies of supersymmetric field theories. The quantities that have been studied in this way are partition functions, expectation values of line operators, and supersymmetric indices. The book also reviews recently discovered connections between SUSY field theories in four dimensions and two-dimensional conformal field theory. These connections have a counterpart in relations between three-dimensional gauge theories and Chern-Simons theory; the book’s closing chapters explore connections with string theory.

Mathematical Quantum Field Theory and Related Topics

Joel S. Feldman,Lon M. Rosen,Université de Montréal. Centre de recherches mathématiques,Natural Sciences and Engineering Research Council Canada
Mathematical Quantum Field Theory and Related Topics Book PDF

Author : Joel S. Feldman,Lon M. Rosen,Université de Montréal. Centre de recherches mathématiques,Natural Sciences and Engineering Research Council Canada
Publisher : American Mathematical Soc.
Page : 280 pages
File Size : 48,8 Mb
Release : 1988
Category : Science
ISBN : 0821860143

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Mathematical Quantum Field Theory and Related Topics by Joel S. Feldman,Lon M. Rosen,Université de Montréal. Centre de recherches mathématiques,Natural Sciences and Engineering Research Council Canada Pdf

Suitable for researchers and advanced graduate students in mathematical physics, this book constitutes the proceedings of a conference on mathematical quantum field theory and related topics. The conference was held at the Centre de Recherches Matheematiques of the Universite de Montreal in September 1987.

Non-perturbative Methods in 2 Dimensional Quantum Field Theory

Elcio Abdalla,M. Cristina B. Abdalla,Klaus Dieter Rothe
Non perturbative Methods in 2 Dimensional Quantum Field Theory Book PDF

Author : Elcio Abdalla,M. Cristina B. Abdalla,Klaus Dieter Rothe
Publisher : World Scientific
Page : 834 pages
File Size : 44,5 Mb
Release : 2001
Category : Science
ISBN : 9789810245962

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Non-perturbative Methods in 2 Dimensional Quantum Field Theory by Elcio Abdalla,M. Cristina B. Abdalla,Klaus Dieter Rothe Pdf

The second edition of Non-Perturbative Methods in Two-Dimensional Quantum Field Theory is an extensively revised version, involving major changes and additions. Although much of the material is special to two dimensions, the techniques used should prove helpful also in the development of techniques applicable in higher dimensions. In particular, the last three chapters of the book will be of direct interest to researchers wanting to work in the field of conformal field theory and strings.This book is intended for students working for their PhD degree and post-doctoral researchers wishing to acquaint themselves with the non-perturbative aspects of quantum field theory.

An Introduction to Symmetry and Supersymmetry in Quantum Field Theory

Jan T. ?opusza?ski
An Introduction to Symmetry and Supersymmetry in Quantum Field Theory Book PDF

Author : Jan T. ?opusza?ski
Publisher : World Scientific
Page : 400 pages
File Size : 43,6 Mb
Release : 1991
Category : Science
ISBN : 9971501619

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An Introduction to Symmetry and Supersymmetry in Quantum Field Theory by Jan T. ?opusza?ski Pdf

This is a set of lecture notes given by the author at the Universities of G”ttingen and Wroclaw. The text presents the axiomatic approach to field theory and studies in depth the concepts of symmetry and supersymmetry and their associated generators, currents and charges. It is intended as a one-semester course for graduate students in the field of mathematical physics and high energy physics.

Fields Medallists' Lectures

Michael Atiyah,Daniel Iagolnitzer
Fields Medallists Lectures Book PDF

Author : Michael Atiyah,Daniel Iagolnitzer
Publisher : World Scientific
Page : 644 pages
File Size : 41,9 Mb
Release : 1997-10-13
Category : Mathematics
ISBN : 9789814497510

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Fields Medallists' Lectures by Michael Atiyah,Daniel Iagolnitzer Pdf

Although the Fields Medal does not have the same public recognition as the Nobel Prizes, they share a similar intellectual standing. It is restricted to one field - that of mathematics - and an age limit of 40 has become an accepted tradition. Mathematics has in the main been interpreted as pure mathematics, and this is not so unreasonable since major contributions in some applied areas can be (and have been) recognized with Nobel Prizes. The restriction to 40 years is of marginal significance, since most mathematicians have made their mark long before this age.A list of Fields Medallists and their contributions provides a bird's eye view of mathematics over the past 60 years. It highlights the areas in which, at various times, greatest progress has been made. This volume does not pretend to be comprehensive, nor is it a historical document. On the other hand, it presents contributions from 22 Fields Medallists and so provides a highly interesting and varied picture.The contributions themselves represent the choice of the individual Medallists. In some cases the articles relate directly to the work for which the Fields Medals were awarded. In other cases new articles have been produced which relate to more current interests of the Medallists. This indicates that while Fields Medallists must be under 40 at the time of the award, their mathematical development goes well past this age. In fact the age limit of 40 was chosen so that young mathematicians would be encouraged in their future work.The Fields Medallists' Lectures is now available on CD-ROM. Sections can be accessed at the touch of a button, and similar topics grouped together using advanced keyword searches.

Fields Medallists' Lectures, 2nd Edition

Michael Atiyah,Daniel Iagolnitzer
Fields Medallists Lectures 2nd Edition Book PDF

Author : Michael Atiyah,Daniel Iagolnitzer
Publisher : World Scientific
Page : 824 pages
File Size : 46,5 Mb
Release : 2003-11-03
Category : Mathematics
ISBN : 9789814486804

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Fields Medallists' Lectures, 2nd Edition by Michael Atiyah,Daniel Iagolnitzer Pdf

Although the Fields Medal does not have the same public recognition as the Nobel Prizes, they share a similar intellectual standing. It is restricted to one field — that of mathematics — and an age limit of 40 has become an accepted tradition. Mathematics has in the main been interpreted as pure mathematics, and this is not so unreasonable since major contributions in some applied areas can be (and have been) recognized with Nobel Prizes.A list of Fields Medallists and their contributions provides a bird's-eye view of mathematics over the past 60 years. It highlights the areas in which, at various times, greatest progress has been made. This volume does not pretend to be comprehensive, nor is it a historical document. On the other hand, it presents contributions from Fields Medallists and so provides a highly interesting and varied picture.The second edition of Fields Medallists' Lectures features additional contributions from the following Medallists: Kunihiko Kodaira (1954), Richard E Borcherds (1998), William T Gowers (1998), Maxim Kontsevich (1998), Curtis T McMullen (1998) and Vladimir Voevodsky (2002).