Evaluating Feynman Integrals
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Evaluating Feynman Integrals
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Author : Vladimir A. Smirnov
language : en
Publisher: Springer
Release Date : 2005-02-28
Evaluating Feynman Integrals written by Vladimir A. Smirnov and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-02-28 with Science categories.
The problem of evaluating Feynman integrals over loop momenta has existed from the early days of perturbative quantum field theory. Although a great variety of methods for evaluating Feynman integrals has been developed over a span of more than fifty years, this book is a first attempt to summarize them. Evaluating Feynman Integrals characterizes the most powerful methods, in particular those used for recent, quite sophisticated calculations, and then illustrates them with numerous examples, starting from very simple ones and progressing to nontrivial examples.
Feynman Integral Calculus
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Author : Vladimir A. Smirnov
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-11-15
Feynman Integral Calculus written by Vladimir A. Smirnov and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-15 with Science categories.
The goal of the book is to summarize those methods for evaluating Feynman integrals that have been developed over a span of more than fifty years. The book characterizes the most powerful methods and illustrates them with numerous examples starting from very simple ones and progressing to nontrivial examples. The book demonstrates how to choose adequate methods and combine evaluation methods in a non-trivial way. The most powerful methods are characterized and then illustrated through numerous examples. This is an updated textbook version of the previous book (Evaluating Feynman integrals, STMP 211) of the author.
Feynman Integral Calculus
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Author : Vladimir A. Smirnov
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-08-02
Feynman Integral Calculus written by Vladimir A. Smirnov and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-08-02 with Mathematics categories.
The goal of the book is to summarize those methods for evaluating Feynman integrals that have been developed over a span of more than fifty years. The book characterizes the most powerful methods and illustrates them with numerous examples starting from very simple ones and progressing to nontrivial examples. The book demonstrates how to choose adequate methods and combine evaluation methods in a non-trivial way. The most powerful methods are characterized and then illustrated through numerous examples. This is an updated textbook version of the previous book (Evaluating Feynman integrals, STMP 211) of the author.
Math With Bad Drawings
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Author : Ben Orlin
language : en
Publisher: Hachette UK
Release Date : 2018-09-18
Math With Bad Drawings written by Ben Orlin and has been published by Hachette UK this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-09-18 with Mathematics categories.
A hilarious reeducation in mathematics-full of joy, jokes, and stick figures-that sheds light on the countless practical and wonderful ways that math structures and shapes our world. In Math With Bad Drawings, Ben Orlin reveals to us what math actually is; its myriad uses, its strange symbols, and the wild leaps of logic and faith that define the usually impenetrable work of the mathematician. Truth and knowledge come in multiple forms: colorful drawings, encouraging jokes, and the stories and insights of an empathetic teacher who believes that math should belong to everyone. Orlin shows us how to think like a mathematician by teaching us a brand-new game of tic-tac-toe, how to understand an economic crises by rolling a pair of dice, and the mathematical headache that ensues when attempting to build a spherical Death Star. Every discussion in the book is illustrated with Orlin's trademark "bad drawings," which convey his message and insights with perfect pitch and clarity. With 24 chapters covering topics from the electoral college to human genetics to the reasons not to trust statistics, Math with Bad Drawings is a life-changing book for the math-estranged and math-enamored alike.
Analytic Tools For Feynman Integrals
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Author : Vladimir A. Smirnov
language : en
Publisher: Springer
Release Date : 2013-01-16
Analytic Tools For Feynman Integrals written by Vladimir A. Smirnov and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-01-16 with Science categories.
The goal of this book is to describe the most powerful methods for evaluating multiloop Feynman integrals that are currently used in practice. This book supersedes the author’s previous Springer book “Evaluating Feynman Integrals” and its textbook version “Feynman Integral Calculus.” Since the publication of these two books, powerful new methods have arisen and conventional methods have been improved on in essential ways. A further qualitative change is the fact that most of the methods and the corresponding algorithms have now been implemented in computer codes which are often public. In comparison to the two previous books, three new chapters have been added: One is on sector decomposition, while the second describes a new method by Lee. The third new chapter concerns the asymptotic expansions of Feynman integrals in momenta and masses, which were described in detail in another Springer book, “Applied Asymptotic Expansions in Momenta and Masses,” by the author. This chapter describes, on the basis of papers that appeared after the publication of said book, how to algorithmically discover the regions relevant to a given limit within the strategy of expansion by regions. In addition, the chapters on the method of Mellin-Barnes representation and on the method of integration by parts have been substantially rewritten, with an emphasis on the corresponding algorithms and computer codes.
Elliptic Integrals Elliptic Functions And Modular Forms In Quantum Field Theory
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Author : Johannes Blümlein
language : en
Publisher: Springer
Release Date : 2019-01-30
Elliptic Integrals Elliptic Functions And Modular Forms In Quantum Field Theory written by Johannes Blümlein and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-01-30 with Computers categories.
This book includes review articles in the field of elliptic integrals, elliptic functions and modular forms intending to foster the discussion between theoretical physicists working on higher loop calculations and mathematicians working in the field of modular forms and functions and analytic solutions of higher order differential and difference equations.
Path Integrals And Quantum Processes
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Author : Mark S. Swanson
language : en
Publisher: Academic Press
Release Date : 2012-12-02
Path Integrals And Quantum Processes written by Mark S. Swanson and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-02 with Science categories.
In a clearly written and systematic presentation, Path Integrals and Quantum Processes covers all concepts necessary to understand the path integral approach to calculating transition elements, partition functions, and source functionals. The book, which assumes only a familiarity with quantum mechanics, is ideal for use as a supplemental textbook in quantum mechanics and quantum field theory courses. Graduate and post-graduate students who are unfamiliar with the path integral will also benefit from this contemporary text. Exercise sets are interspersed throughout the text to facilitate self-study. - Explicates the relationship between the operator and path integral formulations of quantum mechanics and quantum field theory - Provides a systematic and detailed presentation of Grassmann variables - Covers Dirac's method of constraints and the relationship of ghosts, gauge invariance, and gauge conditions in gauge field theory - Includes applications to statistical mechanics, the effective action and potential, and anomaly analysis
Applied Asymptotic Expansions In Momenta And Masses
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Author : Vladimir A. Smirnov
language : en
Publisher: Springer
Release Date : 2003-07-01
Applied Asymptotic Expansions In Momenta And Masses written by Vladimir A. Smirnov and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-07-01 with Science categories.
'The sturgeon they sent was second grade fresh,' said the barman. 'Really, what nonsense/' 'Why nonsense?' '"Second grade fresh" that's what I call nonsense/ There's only one degree of freshness the first, and it's the last) (M. A. Bulgakov, The Master and Margarita) The goal of this book is to describe in detail how Feynman integrals can be expanded in suitable parameters, when various momenta or masses are small or large. In a narrow sense, this problem is connected with practical calcula tions. In a situation where a given Feynman integral depends on parameters of very different scales, a natural idea is to replace it by a sufficiently large number of terms of an expansion of it in ratios of small and large scales. It will be explained how this problem of expansion can be systematically solved, by formulating universal prescriptions that express terms of the expansion by using the original Feynman integral with its integrand expanded into a Taylor series in appropriate momenta and masses. It turns out that knowledge of the structure of the asymptotic expansion at the diagrammatic level is a key point in understanding how to perform expansions at the operator level. There are various examples of these ex pansions: the operator product expansion, the large mass expansion, Heavy Quark Effective Theory, Non Relativistic QCD, etc. Each of them serves as a realization of the factorization of contributions of different scales.
Inside Interesting Integrals
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Author : Paul J. Nahin
language : en
Publisher: Springer Nature
Release Date : 2020-06-27
Inside Interesting Integrals written by Paul J. Nahin and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-06-27 with Science categories.
What’s the point of calculating definite integrals since you can’t possibly do them all? What makes doing the specific integrals in this book of value aren’t the specific answers we’ll obtain, but rather the methods we’ll use in obtaining those answers; methods you can use for evaluating the integrals you will encounter in the future. This book, now in its second edition, is written in a light-hearted manner for students who have completed the first year of college or high school AP calculus and have just a bit of exposure to the concept of a differential equation. Every result is fully derived. If you are fascinated by definite integrals, then this is a book for you. New material in the second edition includes 25 new challenge problems and solutions, 25 new worked examples, simplified derivations, and additional historical discussion.
Path Integrals In Quantum Mechanics Statistics Polymer Physics And Financial Markets
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Author : Hagen Kleinert
language : en
Publisher: World Scientific
Release Date : 2009
Path Integrals In Quantum Mechanics Statistics Polymer Physics And Financial Markets written by Hagen Kleinert and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009 with Business & Economics categories.
Topological restrictions. These are relevant to the understanding of the statistical properties of elementary particles and the entanglement phenomena in polymer physics and biophysics. The Chern-Simons theory of particles with fractional statistics (anyons) is introduced and applied to explain the fractional quantum Hall effect." "The relevance of path integrals to financial markets is discussed, and improvements of the famous Black-Scholes formula for option prices are developed which account for the fact that large market fluctuations occur much more frequently than in Gaussian distributions." --Book Jacket.