Motives, Quantum Field Theory, and Pseudodifferential Operators - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Motives, Quantum Field Theory, and Pseudodifferential Operators write by Alan L. Carey. This book was released on 2010. Motives, Quantum Field Theory, and Pseudodifferential Operators available in PDF, EPUB and Kindle. 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
Computer Algebra in Quantum Field Theory - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Computer Algebra in Quantum Field Theory write by Carsten Schneider. This book was released on 2013-10-05. Computer Algebra in Quantum Field Theory available in PDF, EPUB and Kindle. 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
String-Math 2011 - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook String-Math 2011 write by Jonathan Block. This book was released on 2012. String-Math 2011 available in PDF, EPUB and Kindle. 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.
Renormalization and Galois Theories
Renormalization and Galois Theories - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Renormalization and Galois Theories write by Frédéric Fauvet. This book was released on 2009. Renormalization and Galois Theories available in PDF, EPUB and Kindle. 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
Anti-Differentiation and the Calculation of Feynman Amplitudes - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Anti-Differentiation and the Calculation of Feynman Amplitudes write by Johannes Blümlein. This book was released on 2021-11-26. Anti-Differentiation and the Calculation of Feynman Amplitudes available in PDF, EPUB and Kindle. 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.
