computer algebra in quantum field theory integration summation and special functions texts monographs in symbolic computation

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Computer Algebra In Quantum Field Theory

Author : Carsten Schneider
ISBN : 9783709116166
Genre : Science
File Size : 62. 65 MB
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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.

Computer Algebra And Polynomials

Author : Jaime Gutierrez
ISBN : 9783319150819
Genre : Computers
File Size : 24. 3 MB
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Algebra and number theory have always been counted among the most beautiful mathematical areas with deep proofs and elegant results. However, for a long time they were not considered that important in view of the lack of real-life applications. This has dramatically changed: nowadays we find applications of algebra and number theory frequently in our daily life. This book focuses on the theory and algorithms for polynomials over various coefficient domains such as a finite field or ring. The operations on polynomials in the focus are factorization, composition and decomposition, basis computation for modules, etc. Algorithms for such operations on polynomials have always been a central interest in computer algebra, as it combines formal (the variables) and algebraic or numeric (the coefficients) aspects. The papers presented were selected from the Workshop on Computer Algebra and Polynomials, which was held in Linz at the Johann Radon Institute for Computational and Applied Mathematics (RICAM) during November 25-29, 2013, at the occasion of the Special Semester on Applications of Algebra and Number Theory.

Advances In Computer Algebra

Author : Carsten Schneider
ISBN : 9783319732329
Genre : Mathematics
File Size : 52. 28 MB
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This book discusses the latest advances in algorithms for symbolic summation, factorization, symbolic-numeric linear algebra and linear functional equations. It presents a collection of papers on original research topics from the Waterloo Workshop on Computer Algebra (WWCA-2016), a satellite workshop of the International Symposium on Symbolic and Algebraic Computation (ISSAC’2016), which was held at Wilfrid Laurier University (Waterloo, Ontario, Canada) on July 23–24, 2016. This workshop and the resulting book celebrate the 70th birthday of Sergei Abramov (Dorodnicyn Computing Centre of the Russian Academy of Sciences, Moscow), whose highly regarded and inspirational contributions to symbolic methods have become a crucial benchmark of computer algebra and have been broadly adopted by many Computer Algebra systems.

Handbook Of Enumerative Combinatorics

Author : Miklos Bona
ISBN : 9781482220865
Genre : Mathematics
File Size : 24. 38 MB
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Presenting the state of the art, the Handbook of Enumerative Combinatorics brings together the work of today’s most prominent researchers. The contributors survey the methods of combinatorial enumeration along with the most frequent applications of these methods. This important new work is edited by Miklós Bóna of the University of Florida where he is a member of the Academy of Distinguished Teaching Scholars. He received his Ph.D. in mathematics at Massachusetts Institute of Technology in 1997. Miklós is the author of four books and more than 65 research articles, including the award-winning Combinatorics of Permutations. Miklós Bóna is an editor-in-chief for the Electronic Journal of Combinatorics and Series Editor of the Discrete Mathematics and Its Applications Series for CRC Press/Chapman and Hall. The first two chapters provide a comprehensive overview of the most frequently used methods in combinatorial enumeration, including algebraic, geometric, and analytic methods. These chapters survey generating functions, methods from linear algebra, partially ordered sets, polytopes, hyperplane arrangements, and matroids. Subsequent chapters illustrate applications of these methods for counting a wide array of objects. The contributors for this book represent an international spectrum of researchers with strong histories of results. The chapters are organized so readers advance from the more general ones, namely enumeration methods, towards the more specialized ones. Topics include coverage of asymptotic normality in enumeration, planar maps, graph enumeration, Young tableaux, unimodality, log-concavity, real zeros, asymptotic normality, trees, generalized Catalan paths, computerized enumeration schemes, enumeration of various graph classes, words, tilings, pattern avoidance, computer algebra, and parking functions. This book will be beneficial to a wide audience. It will appeal to experts on the topic interested in learning more about the finer points, readers interested in a systematic and organized treatment of the topic, and novices who are new to the field.

Tensor Categories

Author : Pavel Etingof
ISBN : 9781470434410
Genre :
File Size : 66. 63 MB
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Is there a vector space whose dimension is the golden ratio? Of course not—the golden ratio is not an integer! But this can happen for generalizations of vector spaces—objects of a tensor category. The theory of tensor categories is a relatively new field of mathematics that generalizes the theory of group representations. It has deep connections with many other fields, including representation theory, Hopf algebras, operator algebras, low-dimensional topology (in particular, knot theory), homotopy theory, quantum mechanics and field theory, quantum computation, theory of motives, etc. This book gives a systematic introduction to this theory and a review of its applications. While giving a detailed overview of general tensor categories, it focuses especially on the theory of finite tensor categories and fusion categories (in particular, braided and modular ones), and discusses the main results about them with proofs. In particular, it shows how the main properties of finite-dimensional Hopf algebras may be derived from the theory of tensor categories. Many important results are presented as a sequence of exercises, which makes the book valuable for students and suitable for graduate courses. Many applications, connections to other areas, additional results, and references are discussed at the end of each chapter.

Hagenberg Research

Author : Bruno Buchberger
ISBN : 9783642021275
Genre : Computers
File Size : 56. 24 MB
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BrunoBuchberger This book is a synopsis of basic and applied research done at the various re search institutions of the Softwarepark Hagenberg in Austria. Starting with 15 coworkers in my Research Institute for Symbolic Computation (RISC), I initiated the Softwarepark Hagenberg in 1987 on request of the Upper Aus trian Government with the objective of creating a scienti?c, technological, and economic impulse for the region and the international community. In the meantime, in a joint e?ort, the Softwarepark Hagenberg has grown to the current (2009) size of over 1000 R&D employees and 1300 students in six research institutions, 40 companies and 20 academic study programs on the bachelor, master’s and PhD level. The goal of the Softwarepark Hagenberg is innovation of economy in one of the most important current technologies: software. It is the message of this book that this can only be achieved and guaranteed long term by “watering the root”, namely emphasis on research, both basic and applied. In this book, we summarize what has been achieved in terms of research in the various research institutions in the Softwarepark Hagenberg and what research vision we have for the imminent future. When I founded the Softwarepark Hagenberg, in addition to the “watering the root” principle, I had the vision that such a technology park can only prosper if we realize the “magic triangle”, i.e. the close interaction of research, academic education, and business applications at one site, see Figure 1.

Quantum Gravity

Author : Carlo Rovelli
ISBN : 9781139456159
Genre : Science
File Size : 35. 21 MB
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Quantum gravity is perhaps the most important open problem in fundamental physics. It is the problem of merging quantum mechanics and general relativity, the two great conceptual revolutions in the physics of the twentieth century. The loop and spinfoam approach, presented in this 2004 book, is one of the leading research programs in the field. The first part of the book discusses the reformulation of the basis of classical and quantum Hamiltonian physics required by general relativity. The second part covers the basic technical research directions. Appendices include a detailed history of the subject of quantum gravity, hard-to-find mathematical material, and a discussion of some philosophical issues raised by the subject. This fascinating text is ideal for graduate students entering the field, as well as researchers already working in quantum gravity. It will also appeal to philosophers and other scholars interested in the nature of space and time.

Quantum Mechanics

Author : Julian Schwinger
ISBN : OCLC:439621390
Genre :
File Size : 27. 33 MB
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Ontological Aspects Of Quantum Field Theory

Author : Meinard Kuhlmann
ISBN : 9789814487337
Genre : Science
File Size : 36. 38 MB
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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

Quantum Field Theory And The Standard Model

Author : Matthew D. Schwartz
ISBN : 9781107034730
Genre : Science
File Size : 22. 87 MB
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Modern introduction to quantum field theory for graduates, providing intuitive, physical explanations supported by real-world applications and homework problems.

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