Computer Algebra in Quantum Field Theory PDF Download
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Author: Carsten Schneider
Publisher: Springer Science & Business Media
ISBN: 3709116163
Category : Science
Languages : en
Pages : 422
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Book Description
The book focuses on advanced computer algebra methods and special functions that have striking applications in the context of quantum field theory. It presents the state of the art and new methods for (infinite) multiple sums, multiple integrals, in particular Feynman integrals, difference and differential equations in the format of survey articles. The presented techniques emerge from interdisciplinary fields: mathematics, computer science and theoretical physics; the articles are written by mathematicians and physicists with the goal that both groups can learn from the other field, including most recent developments. Besides that, the collection of articles also serves as an up-to-date handbook of available algorithms/software that are commonly used or might be useful in the fields of mathematics, physics or other sciences.
Author: Carsten Schneider
Publisher: Springer Science & Business Media
ISBN: 3709116163
Category : Science
Languages : en
Pages : 422
Get Book
Book Description
The book focuses on advanced computer algebra methods and special functions that have striking applications in the context of quantum field theory. It presents the state of the art and new methods for (infinite) multiple sums, multiple integrals, in particular Feynman integrals, difference and differential equations in the format of survey articles. The presented techniques emerge from interdisciplinary fields: mathematics, computer science and theoretical physics; the articles are written by mathematicians and physicists with the goal that both groups can learn from the other field, including most recent developments. Besides that, the collection of articles also serves as an up-to-date handbook of available algorithms/software that are commonly used or might be useful in the fields of mathematics, physics or other sciences.
Author: W.-H. Steeb
Publisher: World Scientific
ISBN: 9814307173
Category : Mathematics
Languages : en
Pages : 245
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Book Description
This book collects standard and advanced methods in quantum mechanics and implements them using SymbolicC++ and Maxima, two popular computer algebra packages. Throughout, the sample programs and their outputs are accompanied with explantory text of the underlying mathematics and physics explained in detail. Selected problems have also been implemented using two other popular packages --- Mathematica and Maple --- while some problems are implemented in C++. --
Author: Edson de Faria
Publisher: Cambridge University Press
ISBN: 1139489801
Category : Science
Languages : en
Pages :
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Book Description
Over the last century quantum field theory has made a significant impact on the formulation and solution of mathematical problems and inspired powerful advances in pure mathematics. However, most accounts are written by physicists, and mathematicians struggle to find clear definitions and statements of the concepts involved. This graduate-level introduction presents the basic ideas and tools from quantum field theory to a mathematical audience. Topics include classical and quantum mechanics, classical field theory, quantization of classical fields, perturbative quantum field theory, renormalization, and the standard model. The material is also accessible to physicists seeking a better understanding of the mathematical background, providing the necessary tools from differential geometry on such topics as connections and gauge fields, vector and spinor bundles, symmetries and group representations.
Author: Damien Calaque
Publisher: Springer
ISBN: 3319099493
Category : Science
Languages : en
Pages : 572
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Book Description
Despite its long history and stunning experimental successes, the mathematical foundation of perturbative quantum field theory is still a subject of ongoing research. This book aims at presenting some of the most recent advances in the field, and at reflecting the diversity of approaches and tools invented and currently employed. Both leading experts and comparative newcomers to the field present their latest findings, helping readers to gain a better understanding of not only quantum but also classical field theories. Though the book offers a valuable resource for mathematicians and physicists alike, the focus is more on mathematical developments. This volume consists of four parts: The first Part covers local aspects of perturbative quantum field theory, with an emphasis on the axiomatization of the algebra behind the operator product expansion. The second Part highlights Chern-Simons gauge theories, while the third examines (semi-)classical field theories. In closing, Part 4 addresses factorization homology and factorization algebras.
Author: Michael Creutz
Publisher: World Scientific
ISBN: 9789810209407
Category : Science
Languages : en
Pages : 448
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Book Description
This book provides an overview of recent progress in computer simulations of nonperturbative phenomena in quantum field theory, particularly in the context of the lattice approach. It is a collection of extensive self-contained reviews of various subtopics, including algorithms, spectroscopy, finite temperature physics, Yukawa and chiral theories, bounds on the Higgs meson mass, the renormalization group, and weak decays of hadrons.Physicists with some knowledge of lattice gauge ideas will find this book a useful and interesting source of information on the recent developments in the field.
Author: Karen Yeats
Publisher: Springer
ISBN: 3319475517
Category : Science
Languages : en
Pages : 120
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Book Description
This book explores combinatorial problems and insights in quantum field theory. It is not comprehensive, but rather takes a tour, shaped by the author’s biases, through some of the important ways that a combinatorial perspective can be brought to bear on quantum field theory. Among the outcomes are both physical insights and interesting mathematics. The book begins by thinking of perturbative expansions as kinds of generating functions and then introduces renormalization Hopf algebras. The remainder is broken into two parts. The first part looks at Dyson-Schwinger equations, stepping gradually from the purely combinatorial to the more physical. The second part looks at Feynman graphs and their periods. The flavour of the book will appeal to mathematicians with a combinatorics background as well as mathematical physicists and other mathematicians.
Author: Romeo Brunetti
Publisher: Springer
ISBN: 3319213539
Category : Science
Languages : en
Pages : 453
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Book Description
This text focuses on the algebraic formulation of quantum field theory, from the introductory aspects to the applications to concrete problems of physical interest. The book is divided in thematic chapters covering both introductory and more advanced topics. These include the algebraic, perturbative approach to interacting quantum field theories, algebraic quantum field theory on curved spacetimes (from its structural aspects to the applications in cosmology and to the role of quantum spacetimes), algebraic conformal field theory, the Kitaev's quantum double model from the point of view of local quantum physics and constructive aspects in relation to integrable models and deformation techniques. The book is addressed to master and graduate students both in mathematics and in physics, who are interested in learning the structural aspects and the applications of algebraic quantum field theory.
Author: Willi-hans Steeb
Publisher:
ISBN: 9789814447041
Category :
Languages : en
Pages : 201
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Book Description
Author: Jürg Fröhlich
Publisher: Springer
ISBN: 3540476113
Category : Mathematics
Languages : en
Pages : 438
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Book Description
This book reviews recent results on low-dimensional quantum field theories and their connection with quantum group theory and the theory of braided, balanced tensor categories. It presents detailed, mathematically precise introductions to these subjects and then continues with new results. Among the main results are a detailed analysis of the representation theory of U (sl ), for q a primitive root of unity, and a semi-simple quotient thereof, a classfication of braided tensor categories generated by an object of q-dimension less than two, and an application of these results to the theory of sectors in algebraic quantum field theory. This clarifies the notion of "quantized symmetries" in quantum fieldtheory. The reader is expected to be familiar with basic notions and resultsin algebra. The book is intended for research mathematicians, mathematical physicists and graduate students.
Author: E. Tirapegui
Publisher: Springer Science & Business Media
ISBN: 9400983689
Category : Science
Languages : en
Pages : 333
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Book Description
It is with great emotion that we present here this volume dedicated to the memory of Bernard Jouvet, Docteur es Sciences, Directeur des Recher ches at the Centre National pour la Recherche Scientifique. The life and the career as a physicist of Professor Jouvet are evoked in the following pages by Professor F. Cerulus, a friend of long standing of Professor Jouvet. The contributions have been written by physicists who were friends, collaborators or former students of Professor Jouvet. I express here my gratitude for their contributions. I wish also to thank Mrs. France Jouvet for her kind help in the realiza tion of this book. Without her support this would have been impossible. I am also especially indebted to Professor M. Flato for his constant encouragement and kind cooperation, and to F. Langouche and D. Roekaerts for their generous help in the preparation of this volume. E. TIRAPEGUI TABLE OF CONTENTS FOREWORD VII BIOGRAPHICAL SKETCH XI XIX LIST OF SELECTED SCIENTIFIC PUBLICA TIONS PART ONE: FIELD THEORY AND QUANTIZATION C. BECCHI, A. ROUET and R. sToRA/Renormalizable Theories with Symmetry Breaking 3 J. CALMET and A. VISCONTI/Computing Methods in Quantum Electrodynamics 33 GERARD CLEMENT/Classical Mechanics of Autocomposite Particles 59 s. DEsER/Exclusion of Static Solutions in Gravity-Matter Coupling 77 D. ARNAL, J.C. COR TET, M. FLATO and D. STERNHEIMER/ Star-Products: Quantization and Representations without Operators 85 R. GASTMANs/High Energy Tests of Quantum Electrodynamics 113 L. GOMBEROFF and E.K.
