Vladimir A. Smirnov's Books

Evaluating Feynman Integrals

By: Vladimir A. Smirnov

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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.

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251

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Springer

Published Date

ISBN 10

3540447032

ISBN 13

9783540447030

Feynman Integral Calculus

By: Vladimir A. Smirnov

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Feynman Integral Calculus

By: Vladimir A. Smirnov

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.

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288

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Springer Science & Business Media

Published Date

ISBN 10

3540306102

ISBN 13

9783540306108

Analytic Tools for Feynman Integrals

By: Vladimir A. Smirnov

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Analytic Tools for Feynman Integrals

By: Vladimir A. Smirnov

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.

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Page Count

299

Publisher

Springer

Published Date

ISBN 10

3642348866

ISBN 13

9783642348860

Applied Asymptotic Expansions in Momenta and Masses

By: Vladimir A. Smirnov

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Applied Asymptotic Expansions in Momenta and Masses

By: Vladimir A. Smirnov

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.

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Page Count

270

Publisher

Springer

Published Date

ISBN 10

3540445749

ISBN 13

9783540445746

Persian Art

By: Vladimir Lukonin,Anatoly Ivanov

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Persian Art

By: Vladimir Lukonin,Anatoly Ivanov

Housed in the Hermitage Museum along with other institutes, libraries, and museums in Russia and the republics of the former Soviet Union are some of the most magnificent treasures of Persian Art. For the most part, many of these works have been lost, but have been catalogued and published here for the first time with an unsurpassed selection of colour plates. In a comprehensive introduction, Vladimir Lukonin, Director of the Oriental Art section of the Hermitage Museum, and his colleague Anatoli Ivanov have broadly documented the major developments of Persian Art: from the first signs of civilisation on the plains of Iran around the 10th century BCE through the early 20th century. In the second part of the book they have catalogued Persian Art giving locations, origins, descriptions, and artist biographies where available. Persian Art demonstrates a common theme which runs through the art of the region over the past three millennia. Despite many religious and political upheavals, Persian Art ?? whether in its architecture, sculpture, frescoes, miniatures, porcelain, fabrics, or rugs; whether in the work of the humble craftsmen or the high art of court painters ?? displays the delicate touch and subtle refinement which has had a profound influence on art throughout the world.

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256

Publisher

Parkstone International

Published Date

ISBN 10

1780428936

ISBN 13

9781780428932

Feynman Integral Calculus

By: Vladimir A. Smirnov

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Feynman Integral Calculus

By: Vladimir A. Smirnov

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Solve jigsaw puzzle

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Page Count

288

Publisher

Springer Science & Business Media

Published Date

ISBN 10

3540306102

ISBN 13

9783540306108

Book's by Vladimir A. Smirnov

Evaluating Feynman Integrals

Evaluating Feynman Integrals

Feynman Integral Calculus

Feynman Integral Calculus

Analytic Tools for Feynman Integrals

Analytic Tools for Feynman Integrals

Applied Asymptotic Expansions in Momenta and Masses

Applied Asymptotic Expansions in Momenta and Masses

Persian Art

Persian Art

Feynman Integral Calculus

Feynman Integral Calculus

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