Dmitri Gitman's Books

Quantization of Fields with Constraints

By: Dmitri Gitman,Igor V. Tyutin

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Quantization of Fields with Constraints

By: Dmitri Gitman,Igor V. Tyutin

Gauge field theories underlie all models now used in elementary particle physics. These theories refer to the class of singular theories which are also theories with constraints. The quantization of singular theories remains one of the key problems of quantum field theory and is being intensively discussed in the literature. This book is an attempt to fill the need for a comprehensive analysis of this problem, which has not heretofore been met by the available monographs and reviews. The main topics are canonical quantization and the path integral method. In addition, the Lagrangian BRST quantization is completely described, for the first time in a monograph. The book also presents a number of original results obtained by the authors, in particular, a complete description of the physical sector of an arbitrary gauge theory, quantization of singular theories with higher theories with time-dependent constraints, and correct derivatives, quantization of canonical quantization of theories of a relativistic point-like particle. As a general illustration we present quantization of field theories such as electrodynamics, Yang-Mills theory, and gravity. It should be noted that this monograph is aimed not only at giving the reader the rules of quantization according to the principle "if you do it this way, it will be good", but also at presenting strong arguments based on the modem interpretation of the classical and quantum theories which show that these methods· are the natural, if not the only possible ones.

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301

Publisher

Springer Science & Business Media

Published Date

ISBN 10

364283938X

ISBN 13

9783642839382

A Heuristic Approach to Possibilistic Clustering: Algorithms and Applications

By: Dmitri A. Viattchenin

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A Heuristic Approach to Possibilistic Clustering: Algorithms and Applications

By: Dmitri A. Viattchenin

The present book outlines a new approach to possibilistic clustering in which the sought clustering structure of the set of objects is based directly on the formal definition of fuzzy cluster and the possibilistic memberships are determined directly from the values of the pairwise similarity of objects. The proposed approach can be used for solving different classification problems. Here, some techniques that might be useful at this purpose are outlined, including a methodology for constructing a set of labeled objects for a semi-supervised clustering algorithm, a methodology for reducing analyzed attribute space dimensionality and a methods for asymmetric data processing. Moreover, a technique for constructing a subset of the most appropriate alternatives for a set of weak fuzzy preference relations, which are defined on a universe of alternatives, is described in detail, and a method for rapidly prototyping the Mamdani’s fuzzy inference systems is introduced. This book addresses engineers, scientists, professors, students and post-graduate students, who are interested in and work with fuzzy clustering and its applications

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238

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Springer

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ISBN 10

3642355366

ISBN 13

9783642355363

Operators, Geometry and Quanta

Methods of Spectral Geometry in Quantum Field Theory

By: Dmitri Fursaev,Dmitri Vassilevich

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Operators, Geometry and Quanta

Methods of Spectral Geometry in Quantum Field Theory

By: Dmitri Fursaev,Dmitri Vassilevich

This book gives a detailed and self-contained introduction into the theory of spectral functions, with an emphasis on their applications to quantum field theory. All methods are illustrated with applications to specific physical problems from the forefront of current research, such as finite-temperature field theory, D-branes, quantum solitons and noncommutativity. In the first part of the book, necessary background information on differential geometry and quantization, including less standard material, is collected. The second part of the book contains a detailed description of main spectral functions and methods of their calculation. In the third part, the theory is applied to several examples (D-branes, quantum solitons, anomalies, noncommutativity). This book addresses advanced graduate students and researchers in mathematical physics with basic knowledge of quantum field theory and differential geometry. The aim is to prepare readers to use spectral functions in their own research, in particular in relation to heat kernels and zeta functions.

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294

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Springer Science & Business Media

Published Date

ISBN 10

9400702051

ISBN 13

9789400702059

Quantization of Fields with Constraints

By: Dmitri Gitman,Igor V. Tyutin

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Quantization of Fields with Constraints

By: Dmitri Gitman,Igor V. Tyutin

Average ratings

N/A

Write a review

Solve jigsaw puzzle

Age

Page Count

301

Publisher

Springer Science & Business Media

Published Date

ISBN 10

364283938X

ISBN 13

9783642839382

Book's by Dmitri Gitman

Quantization of Fields with Constraints

Quantization of Fields with Constraints

A Heuristic Approach to Possibilistic Clustering: Algorithms and Applications

A Heuristic Approach to Possibilistic Clustering: Algorithms and Applications

Operators, Geometry and Quanta

Operators, Geometry and Quanta

Quantization of Fields with Constraints

Quantization of Fields with Constraints

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