Motives Quantum Field Theory And Pseudodifferential Operators

Motives Quantum Field Theory And Pseudodifferential Operators Book in PDF, ePub and Kindle version is available to download in english. Read online anytime anywhere directly from your device. Click on the download button below to get a free pdf file of Motives Quantum Field Theory And Pseudodifferential Operators book. This book definitely worth reading, it is an incredibly well-written.

Motives, Quantum Field Theory, and Pseudodifferential Operators

Alan L. Carey
Motives Quantum Field Theory and Pseudodifferential Operators Book PDF

Author : Alan L. Carey
Publisher : American Mathematical Soc.
Page : 361 pages
File Size : 48,9 Mb
Release : 2010
Category : Mathematics
ISBN : 9780821851999

Get Book

Motives, Quantum Field Theory, and Pseudodifferential Operators by Alan L. Carey Pdf

This volume contains articles related to the conference ``Motives, Quantum Field Theory, and Pseudodifferntial Operators'' held at Boston University in June 2008, with partial support from the Clay Mathematics Institute, Boston University, and the National Science Foundation. There are deep but only partially understood connections between the three conference fields, so this book is intended both to explain the known connections and to offer directions for further research. In keeping with the organization of the conference, this book contains introductory lectures on each of the conference themes and research articles on current topics in these fields. The introductory lectures are suitable for graduate students and new Ph.D.'s in both mathematics and theoretical physics, as well as for senior researchers, since few mathematicians are expert in any two of the conference areas. Among the topics discussed in the introductory lectures are the appearance of multiple zeta values both as periods of motives and in Feynman integral calculations in perturbative QFT, the use of Hopf algebra techniques for renormalization in QFT, and regularized traces of pseudodifferential operators. The motivic interpretation of multiple zeta values points to a fundamental link between motives and QFT, and there are strong parallels between regularized traces and Feynman integral techniques. The research articles cover a range of topics in areas related to the conference themes, including geometric, Hopf algebraic, analytic, motivic and computational aspects of quantum field theory and mirror symmetry. There is no unifying theory of the conference areas at present, so the research articles present the current state of the art pointing towards such a unification.

Computer Algebra in Quantum Field Theory

Carsten Schneider,Johannes Blümlein
Computer Algebra in Quantum Field Theory Book PDF

Author : Carsten Schneider,Johannes Blümlein
Publisher : Springer Science & Business Media
Page : 422 pages
File Size : 47,8 Mb
Release : 2013-10-05
Category : Science
ISBN : 9783709116166

Get Book

Computer Algebra in Quantum Field Theory by Carsten Schneider,Johannes Blümlein Pdf

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.

String-Math 2011

Jonathan Block
String Math 2011 Book PDF

Author : Jonathan Block
Publisher : American Mathematical Soc.
Page : 506 pages
File Size : 46,7 Mb
Release : 2012
Category : Mathematics
ISBN : 9780821872956

Get Book

String-Math 2011 by Jonathan Block Pdf

The nature of interactions between mathematicians and physicists has been thoroughly transformed in recent years. String theory and quantum field theory have contributed a series of profound ideas that gave rise to entirely new mathematical fields and revitalized older ones. The influence flows in both directions, with mathematical techniques and ideas contributing crucially to major advances in string theory. A large and rapidly growing number of both mathematicians and physicists are working at the string-theoretic interface between the two academic fields. The String-Math conference series aims to bring together leading mathematicians and mathematically minded physicists working in this interface. This volume contains the proceedings of the inaugural conference in this series, String-Math 2011, which was held June 6-11, 2011, at the University of Pennsylvania.

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 : 48,5 Mb
Release : 2003-10-14
Category : Science
ISBN : 9789814486033

Get Book

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.

Renormalization and Galois Theories

Frédéric Fauvet,Jean-Pierre Ramis
Renormalization and Galois Theories Book PDF

Author : Frédéric Fauvet,Jean-Pierre Ramis
Publisher : European Mathematical Society
Page : 284 pages
File Size : 53,8 Mb
Release : 2009
Category : Mathematics
ISBN : 3037190736

Get Book

Renormalization and Galois Theories by Frédéric Fauvet,Jean-Pierre Ramis Pdf

This volume is the outcome of a CIRM Workshop on Renormalization and Galois Theories held in Luminy, France, in March 2006. The subject of this workshop was the interaction and relationship between four currently very active areas: renormalization in quantum field theory (QFT), differential Galois theory, noncommutative geometry, motives and Galois theory. The last decade has seen a burst of new techniques to cope with the various mathematical questions involved in QFT, with notably the development of a Hopf-algebraic approach and insights into the classes of numbers and special functions that systematically appear in the calculations of perturbative QFT (pQFT). The analysis of the ambiguities of resummation of the divergent series of pQFT, an old problem, has been renewed, using recent results on Gevrey asymptotics, generalized Borel summation, Stokes phenomenon and resurgent functions. The purpose of the present book is to highlight, in the context of renormalization, the convergence of these various themes, orchestrated by diverse Galois theories. It contains three lecture courses together with five research articles and will be useful to both researchers and graduate students in mathematics and physics.

Anti-Differentiation and the Calculation of Feynman Amplitudes

Johannes Blümlein,Carsten Schneider
Anti Differentiation and the Calculation of Feynman Amplitudes Book PDF

Author : Johannes Blümlein,Carsten Schneider
Publisher : Springer Nature
Page : 551 pages
File Size : 49,6 Mb
Release : 2021-11-26
Category : Science
ISBN : 9783030802196

Get Book

Anti-Differentiation and the Calculation of Feynman Amplitudes by Johannes Blümlein,Carsten Schneider Pdf

This volume comprises review papers presented at the Conference on Antidifferentiation and the Calculation of Feynman Amplitudes, held in Zeuthen, Germany, in October 2020, and a few additional invited reviews. The book aims at comprehensive surveys and new innovative results of the analytic integration methods of Feynman integrals in quantum field theory. These methods are closely related to the field of special functions and their function spaces, the theory of differential equations and summation theory. Almost all of these algorithms have a strong basis in computer algebra. The solution of the corresponding problems are connected to the analytic management of large data in the range of Giga- to Terabytes. The methods are widely applicable to quite a series of other branches of mathematics and theoretical physics.

Computer Algebra and Polynomials

Jaime Gutierrez,Josef Schicho,Martin Weimann
Computer Algebra and Polynomials Book PDF

Author : Jaime Gutierrez,Josef Schicho,Martin Weimann
Publisher : Springer
Page : 222 pages
File Size : 45,7 Mb
Release : 2015-01-20
Category : Computers
ISBN : 9783319150819

Get Book

Computer Algebra and Polynomials by Jaime Gutierrez,Josef Schicho,Martin Weimann Pdf

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.

Calabi-Yau Varieties: Arithmetic, Geometry and Physics

Radu Laza,Matthias Schütt,Noriko Yui
Calabi Yau Varieties Arithmetic Geometry and Physics Book PDF

Author : Radu Laza,Matthias Schütt,Noriko Yui
Publisher : Springer
Page : 547 pages
File Size : 40,5 Mb
Release : 2015-08-27
Category : Mathematics
ISBN : 9781493928309

Get Book

Calabi-Yau Varieties: Arithmetic, Geometry and Physics by Radu Laza,Matthias Schütt,Noriko Yui Pdf

This volume presents a lively introduction to the rapidly developing and vast research areas surrounding Calabi–Yau varieties and string theory. With its coverage of the various perspectives of a wide area of topics such as Hodge theory, Gross–Siebert program, moduli problems, toric approach, and arithmetic aspects, the book gives a comprehensive overview of the current streams of mathematical research in the area. The contributions in this book are based on lectures that took place during workshops with the following thematic titles: “Modular Forms Around String Theory,” “Enumerative Geometry and Calabi–Yau Varieties,” “Physics Around Mirror Symmetry,” “Hodge Theory in String Theory.” The book is ideal for graduate students and researchers learning about Calabi–Yau varieties as well as physics students and string theorists who wish to learn the mathematics behind these varieties.

Geometric and Spectral Analysis

Pierre Albin,Dmitry Jakobson, Frédéric Rochon
Geometric and Spectral Analysis Book PDF

Author : Pierre Albin,Dmitry Jakobson, Frédéric Rochon
Publisher : American Mathematical Soc.
Page : 378 pages
File Size : 42,6 Mb
Release : 2014-12-01
Category : Mathematics
ISBN : 9781470410438

Get Book

Geometric and Spectral Analysis by Pierre Albin,Dmitry Jakobson, Frédéric Rochon Pdf

In 2012, the Centre de Recherches Mathématiques was at the center of many interesting developments in geometric and spectral analysis, with a thematic program on Geometric Analysis and Spectral Theory followed by a thematic year on Moduli Spaces, Extremality and Global Invariants. This volume contains original contributions as well as useful survey articles of recent developments by participants from three of the workshops organized during these programs: Geometry of Eigenvalues and Eigenfunctions, held from June 4-8, 2012; Manifolds of Metrics and Probabilistic Methods in Geometry and Analysis, held from July 2-6, 2012; and Spectral Invariants on Non-compact and Singular Spaces, held from July 23-27, 2012. The topics covered in this volume include Fourier integral operators, eigenfunctions, probability and analysis on singular spaces, complex geometry, Kähler-Einstein metrics, analytic torsion, and Strichartz estimates. This book is co-published with the Centre de Recherches Mathématiques.

Evolution Equations

David Ellwood,Igor Rodnianski,Gigliola Staffilani,Jared Wunsch
Evolution Equations Book PDF

Author : David Ellwood,Igor Rodnianski,Gigliola Staffilani,Jared Wunsch
Publisher : American Mathematical Soc.
Page : 587 pages
File Size : 40,7 Mb
Release : 2013-06-26
Category : Mathematics
ISBN : 9780821868614

Get Book

Evolution Equations by David Ellwood,Igor Rodnianski,Gigliola Staffilani,Jared Wunsch Pdf

This volume is a collection of notes from lectures given at the 2008 Clay Mathematics Institute Summer School, held in Zürich, Switzerland. The lectures were designed for graduate students and mathematicians within five years of the Ph.D., and the main focus of the program was on recent progress in the theory of evolution equations. Such equations lie at the heart of many areas of mathematical physics and arise not only in situations with a manifest time evolution (such as linear and nonlinear wave and Schrödinger equations) but also in the high energy or semi-classical limits of elliptic problems. The three main courses focused primarily on microlocal analysis and spectral and scattering theory, the theory of the nonlinear Schrödinger and wave equations, and evolution problems in general relativity. These major topics were supplemented by several mini-courses reporting on the derivation of effective evolution equations from microscopic quantum dynamics; on wave maps with and without symmetries; on quantum N-body scattering, diffraction of waves, and symmetric spaces; and on nonlinear Schrödinger equations at critical regularity. Although highly detailed treatments of some of these topics are now available in the published literature, in this collection the reader can learn the fundamental ideas and tools with a minimum of technical machinery. Moreover, the treatment in this volume emphasizes common themes and techniques in the field, including exact and approximate conservation laws, energy methods, and positive commutator arguments. Titles in this series are co-published with the Clay Mathematics Institute (Cambridge, MA).

Probability and Statistical Physics in Two and More Dimensions

Clay Mathematics Institute. Summer School
Probability and Statistical Physics in Two and More Dimensions Book PDF

Author : Clay Mathematics Institute. Summer School
Publisher : American Mathematical Soc.
Page : 481 pages
File Size : 40,5 Mb
Release : 2012
Category : Mathematics
ISBN : 9780821868638

Get Book

Probability and Statistical Physics in Two and More Dimensions by Clay Mathematics Institute. Summer School Pdf

This volume is a collection of lecture notes for six of the ten courses given in Buzios, Brazil by prominent probabilists at the 2010 Clay Mathematics Institute Summer School, ``Probability and Statistical Physics in Two and More Dimensions'' and at the XIV Brazilian School of Probability. In the past ten to fifteen years, various areas of probability theory related to statistical physics, disordered systems and combinatorics have undergone intensive development. A number of these developments deal with two-dimensional random structures at their critical points, and provide new tools and ways of coping with at least some of the limitations of Conformal Field Theory that had been so successfully developed in the theoretical physics community to understand phase transitions of two-dimensional systems. Included in this selection are detailed accounts of all three foundational courses presented at the Clay school--Schramm-Loewner Evolution and other Conformally Invariant Objects, Noise Sensitivity and Percolation, Scaling Limits of Random Trees and Planar Maps--together with contributions on Fractal and Multifractal properties of SLE and Conformal Invariance of Lattice Models. Finally, the volume concludes with extended articles based on the courses on Random Polymers and Self-Avoiding Walks given at the Brazilian School of Probability during the final week of the school. Together, these notes provide a panoramic, state-of-the-art view of probability theory areas related to statistical physics, disordered systems and combinatorics. Like the lectures themselves, they are oriented towards advanced students and postdocs, but experts should also find much of interest.

Hagenberg Research

Bruno Buchberger,Michael Affenzeller,Alois Ferscha,Michael Haller,Tudor Jebelean,Erich Peter Klement,Peter Paule,Gustav Pomberger,Wolfgang Schreiner,Robert Stubenrauch,Roland Wagner,Gerhard Weiß,Wolfgang Windsteiger
Hagenberg Research Book PDF

Author : Bruno Buchberger,Michael Affenzeller,Alois Ferscha,Michael Haller,Tudor Jebelean,Erich Peter Klement,Peter Paule,Gustav Pomberger,Wolfgang Schreiner,Robert Stubenrauch,Roland Wagner,Gerhard Weiß,Wolfgang Windsteiger
Publisher : Springer Science & Business Media
Page : 490 pages
File Size : 44,9 Mb
Release : 2009-05-29
Category : Computers
ISBN : 9783642021275

Get Book

Hagenberg Research by Bruno Buchberger,Michael Affenzeller,Alois Ferscha,Michael Haller,Tudor Jebelean,Erich Peter Klement,Peter Paule,Gustav Pomberger,Wolfgang Schreiner,Robert Stubenrauch,Roland Wagner,Gerhard Weiß,Wolfgang Windsteiger Pdf

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.

Proceedings of the Conference in Honour of Murray Gell-Mann's 80th Birthday

Harald Fritzsch,K. K. Phua
Proceedings of the Conference in Honour of Murray Gell Mann s 80th Birthday Book PDF

Author : Harald Fritzsch,K. K. Phua
Publisher : World Scientific
Page : 730 pages
File Size : 49,5 Mb
Release : 2011
Category : Science
ISBN : 9789814335607

Get Book

Proceedings of the Conference in Honour of Murray Gell-Mann's 80th Birthday by Harald Fritzsch,K. K. Phua Pdf

The Conference on Quantum Mechanics, Elementary Particles, Quantum Cosmology and Complexity was held in honour of Professor Murray Gell-Mann's 80th birthday in Singapore on 24?26 February 2010. The conference paid tribute to Professor Gell-Mann's great achievements in the elementary particle physics. This notable birthday volume contains the presentations made at the conference by many eminent scientists, including Nobel laureates C N Yang, G 't Hooft and K Wilson. Other invited speakers include G Zweig, N Samios, M Karliner, G Karl, M Shifman, J Ellis, S Adler and A Zichichi. About Murray Gell-Mann Murray Gell-Mann, born September 15, 1929, won the 1969 Nobel Prize in physics for his work on the theory of elementary particles. His contributions span the entire history of particle physics, from the early days of the particle zoo to the modern day QCD. Along the way, even as he proposed new quantum numbers to bring order into the zoo, he had fun in naming them. And thus was born Strangeness, Flavor, Hadrons, Baryons, Leptons, the Eightfold Way, Color, Quarks, Gluons and, with Harald Fritzsch, the standard field theory of strong interactions, Quantum Chromodynamics (QCD). He also proposed with Richard Feynman the V-A theory of beta decay. Gell-Mann discovered the Current Algebra, proposed (with Levy) the sigma model of pions and the see-saw mechanism for the neutrino masses.

A Celebration of Algebraic Geometry

Brendan Hassett,James McKernan,Jason Starr,Ravi Vakil
A Celebration of Algebraic Geometry Book PDF

Author : Brendan Hassett,James McKernan,Jason Starr,Ravi Vakil
Publisher : American Mathematical Soc.
Page : 614 pages
File Size : 51,5 Mb
Release : 2013-09-11
Category : Mathematics
ISBN : 9780821889831

Get Book

A Celebration of Algebraic Geometry by Brendan Hassett,James McKernan,Jason Starr,Ravi Vakil Pdf

This volume resulted from the conference A Celebration of Algebraic Geometry, which was held at Harvard University from August 25-28, 2011, in honor of Joe Harris' 60th birthday. Harris is famous around the world for his lively textbooks and enthusiastic teaching, as well as for his seminal research contributions. The articles are written in this spirit: clear, original, engaging, enlivened by examples, and accessible to young mathematicians. The articles in this volume focus on the moduli space of curves and more general varieties, commutative algebra, invariant theory, enumerative geometry both classical and modern, rationally connected and Fano varieties, Hodge theory and abelian varieties, and Calabi-Yau and hyperkähler manifolds. Taken together, they present a comprehensive view of the long frontier of current knowledge in algebraic geometry. Titles in this series are co-published with the Clay Mathematics Institute (Cambridge, MA).

Topics in Noncommutative Geometry

Guillermo Cortiñas
Topics in Noncommutative Geometry Book PDF

Author : Guillermo Cortiñas
Publisher : American Mathematical Soc.
Page : 289 pages
File Size : 40,9 Mb
Release : 2012
Category : Mathematics
ISBN : 9780821868645

Get Book

Topics in Noncommutative Geometry by Guillermo Cortiñas Pdf

Luis Santalo Winter Schools are organized yearly by the Mathematics Department and the Santalo Mathematical Research Institute of the School of Exact and Natural Sciences of the University of Buenos Aires (FCEN). This volume contains the proceedings of the third Luis Santalo Winter School which was devoted to noncommutative geometry and held at FCEN July 26-August 6, 2010. Topics in this volume concern noncommutative geometry in a broad sense, encompassing various mathematical and physical theories that incorporate geometric ideas to the study of noncommutative phenomena. It explores connections with several areas including algebra, analysis, geometry, topology and mathematical physics. Bursztyn and Waldmann discuss the classification of star products of Poisson structures up to Morita equivalence. Tsygan explains the connections between Kontsevich's formality theorem, noncommutative calculus, operads and index theory. Hoefel presents a concrete elementary construction in operad theory. Meyer introduces the subject of $\mathrm{C}^*$-algebraic crossed products. Rosenberg introduces Kasparov's $KK$-theory and noncommutative tori and includes a discussion of the Baum-Connes conjecture for $K$-theory of crossed products, among other topics. Lafont, Ortiz, and Sanchez-Garcia carry out a concrete computation in connection with the Baum-Connes conjecture. Zuk presents some remarkable groups produced by finite automata. Mesland discusses spectral triples and the Kasparov product in $KK$-theory. Trinchero explores the connections between Connes' noncommutative geometry and quantum field theory. Karoubi demonstrates a construction of twisted $K$-theory by means of twisted bundles. Tabuada surveys the theory of noncommutative motives.