Representations Of The Rotation And Lorentz Groups And Their Applications

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Representations of the Rotation and Lorentz Groups and Their Applications

I. M. Gelfand,R. A. Minlos,Z. Ya. Shapiro
Representations of the Rotation and Lorentz Groups and Their Applications Book PDF

Author : I. M. Gelfand,R. A. Minlos,Z. Ya. Shapiro
Publisher : Courier Dover Publications
Page : 385 pages
File Size : 41,9 Mb
Release : 2018-04-18
Category : Science
ISBN : 9780486823850

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Representations of the Rotation and Lorentz Groups and Their Applications by I. M. Gelfand,R. A. Minlos,Z. Ya. Shapiro Pdf

This monograph on the description and study of representations of the rotation group of three-dimensional space and of the Lorentz group features advanced topics and techniques crucial to many areas of modern theoretical physics. Prerequisites include a familiarity with the differential and integral calculus of several variables and the fundamentals of linear algebra. Suitable for advanced undergraduate and graduate students in mathematical physics, the book is also designed for mathematicians studying the representations of Lie groups, for whom it can serve as an introduction to the general theory of representation. The treatment encompasses all the basic material of the theory of representations used in quantum mechanics. The two-part approach begins with representations of the group of rotations of three-dimensional space, analyzing the rotation group and its representations. The second part, covering representations of the Lorentz group, includes an exploration of relativistic-invariant equations. The text concludes with three helpful supplements and a bibliography.

Representations of the Rotation and Lorentz Groups and Their Applications

R. A. Minlos,Z. Ya Chapiro,Izrail Moiseevitch Gelfand
Representations of the Rotation and Lorentz Groups and Their Applications Book PDF

Author : R. A. Minlos,Z. Ya Chapiro,Izrail Moiseevitch Gelfand
Publisher : Unknown
Page : 366 pages
File Size : 48,5 Mb
Release : 1963
Category : Electronic
ISBN : OCLC:460470313

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Representations of the Rotation and Lorentz Groups and Their Applications by R. A. Minlos,Z. Ya Chapiro,Izrail Moiseevitch Gelfand Pdf

The Rotation and Lorentz Groups and Their Representations for Physicists

K. Srinivasa Rao
The Rotation and Lorentz Groups and Their Representations for Physicists Book PDF

Author : K. Srinivasa Rao
Publisher : John Wiley & Sons
Page : 380 pages
File Size : 50,9 Mb
Release : 1988
Category : Business & Economics
ISBN : 0470210443

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The Rotation and Lorentz Groups and Their Representations for Physicists by K. Srinivasa Rao Pdf

Here is a detailed, self-contained work on the rotation and Lorentz groups and their representations. Treatment of the structure of the groups is elaborate and includes many new results only recently published in journals. The chapter on linear vector spaces is exhaustive yet clear, and the book highlights the fact that all results of the orthosynchronous proper Lorentz group may be obtained from those of the rotation group via complex quaternions. The approach is unified, and special properties and exceptional cases are addressed.

Group Theory and General Relativity

Moshe Carmeli
Group Theory and General Relativity Book PDF

Author : Moshe Carmeli
Publisher : World Scientific
Page : 416 pages
File Size : 53,8 Mb
Release : 2000
Category : Science
ISBN : 1860942342

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Group Theory and General Relativity by Moshe Carmeli Pdf

This is the only book on the subject of group theory and Einstein's theory of gravitation. It contains an extensive discussion on general relativity from the viewpoint of group theory and gauge fields. It also puts together in one volume many scattered, original works, on the use of group theory in general relativity theory. There are twelve chapters in the book. The first six are devoted to rotation and Lorentz groups, and their representations. They include the spinor representation as well as the infinite-dimensional representations. The other six chapters deal with the application of groups -- particularly the Lorentz and the SL(2, C) groups -- to the theory of general relativity. Each chapter is concluded with a set of problems. The topics covered range from the fundamentals of general relativity theory, its formulation as an SL(2, C) gauge theory, to exact solutions of the Einstein gravitational field equations. The important Bondi-Metzner-Sachs group, and its representations, conclude the book The entire book is self-contained in both group theory and general relativity theory, and no prior knowledge of either is assumed. The subject of this book constitutes a relevant link between field theoreticians and general relativity theoreticians, who usually work rather independently of each other. The treatise is highly topical and of real interest to theoretical physicists, general relativists and applied mathematicians. It is invaluable to graduate students and research workers in quantum field theory, general relativity and elementary particle theory.

Lie Groups, Lie Algebras, and Some of Their Applications

Robert Gilmore
Lie Groups Lie Algebras and Some of Their Applications Book PDF

Author : Robert Gilmore
Publisher : Courier Corporation
Page : 610 pages
File Size : 40,7 Mb
Release : 2012-05-23
Category : Mathematics
ISBN : 9780486131566

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Lie Groups, Lie Algebras, and Some of Their Applications by Robert Gilmore Pdf

This text introduces upper-level undergraduates to Lie group theory and physical applications. It further illustrates Lie group theory's role in several fields of physics. 1974 edition. Includes 75 figures and 17 tables, exercises and problems.

Symmetry Groups and Their Applications

Anonim
Symmetry Groups and Their Applications Book PDF

Author : Anonim
Publisher : Academic Press
Page : 431 pages
File Size : 40,6 Mb
Release : 1973-03-02
Category : Mathematics
ISBN : 0080873650

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Symmetry Groups and Their Applications by Anonim Pdf

Symmetry Groups and Their Applications

Engineering Applications of Noncommutative Harmonic Analysis

Gregory S. Chirikjian,Alexander B. Kyatkin
Engineering Applications of Noncommutative Harmonic Analysis Book PDF

Author : Gregory S. Chirikjian,Alexander B. Kyatkin
Publisher : CRC Press
Page : 555 pages
File Size : 45,6 Mb
Release : 2021-02-25
Category : Mathematics
ISBN : 9781000697339

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Engineering Applications of Noncommutative Harmonic Analysis by Gregory S. Chirikjian,Alexander B. Kyatkin Pdf

First published in 2001. The classical Fourier transform is one of the most widely used mathematical tools in engineering. However, few engineers know that extensions of harmonic analysis to functions on groups holds great potential for solving problems in robotics, image analysis, mechanics, and other areas. For those that may be aware of its potential value, there is still no place they can turn to for a clear presentation of the background they need to apply the concept to engineering problems. Engineering Applications of Noncommutative Harmonic Analysis brings this powerful tool to the engineering world. Written specifically for engineers and computer scientists, it offers a practical treatment of harmonic analysis in the context of particular Lie groups (rotation and Euclidean motion). It presents only a limited number of proofs, focusing instead on providing a review of the fundamental mathematical results unknown to most engineers and detailed discussions of specific applications. Advances in pure mathematics can lead to very tangible advances in engineering, but only if they are available and accessible to engineers. Engineering Applications of Noncommutative Harmonic Analysis provides the means for adding this valuable and effective technique to the engineer's toolbox.

Quantum Field Theory III: Gauge Theory

Eberhard Zeidler
Quantum Field Theory III Gauge Theory Book PDF

Author : Eberhard Zeidler
Publisher : Springer Science & Business Media
Page : 1141 pages
File Size : 45,6 Mb
Release : 2011-08-17
Category : Mathematics
ISBN : 9783642224218

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Quantum Field Theory III: Gauge Theory by Eberhard Zeidler Pdf

In this third volume of his modern introduction to quantum field theory, Eberhard Zeidler examines the mathematical and physical aspects of gauge theory as a principle tool for describing the four fundamental forces which act in the universe: gravitative, electromagnetic, weak interaction and strong interaction. Volume III concentrates on the classical aspects of gauge theory, describing the four fundamental forces by the curvature of appropriate fiber bundles. This must be supplemented by the crucial, but elusive quantization procedure. The book is arranged in four sections, devoted to realizing the universal principle force equals curvature: Part I: The Euclidean Manifold as a Paradigm Part II: Ariadne's Thread in Gauge Theory Part III: Einstein's Theory of Special Relativity Part IV: Ariadne's Thread in Cohomology For students of mathematics the book is designed to demonstrate that detailed knowledge of the physical background helps to reveal interesting interrelationships among diverse mathematical topics. Physics students will be exposed to a fairly advanced mathematics, beyond the level covered in the typical physics curriculum. Quantum Field Theory builds a bridge between mathematicians and physicists, based on challenging questions about the fundamental forces in the universe (macrocosmos), and in the world of elementary particles (microcosmos).

Theory Of Spinors: An Introduction

Moshe Carmeli,Shimon Malin
Theory Of Spinors An Introduction Book PDF

Author : Moshe Carmeli,Shimon Malin
Publisher : World Scientific Publishing Company
Page : 228 pages
File Size : 52,6 Mb
Release : 2000-04-12
Category : Science
ISBN : 9789813102767

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Theory Of Spinors: An Introduction by Moshe Carmeli,Shimon Malin Pdf

Spinors are used extensively in physics. It is widely accepted that they are more fundamental than tensors, and the easy way to see this is through the results obtained in general relativity theory by using spinors — results that could not have been obtained by using tensor methods only.The foundation of the concept of spinors is groups; spinors appear as representations of groups. This textbook expounds the relationship between spinors and representations of groups. As is well known, spinors and representations are both widely used in the theory of elementary particles.The authors present the origin of spinors from representation theory, but nevertheless apply the theory of spinors to general relativity theory, and part of the book is devoted to curved space-time applications.Based on lectures given at Ben Gurion University, this textbook is intended for advanced undergraduate and graduate students in physics and mathematics, as well as being a reference for researchers.

Symmetries and Group Theory in Particle Physics

Giovanni Costa,Gianluigi Fogli
Symmetries and Group Theory in Particle Physics Book PDF

Author : Giovanni Costa,Gianluigi Fogli
Publisher : Springer
Page : 291 pages
File Size : 45,6 Mb
Release : 2012-02-03
Category : Science
ISBN : 9783642154829

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Symmetries and Group Theory in Particle Physics by Giovanni Costa,Gianluigi Fogli Pdf

Symmetries, coupled with the mathematical concept of group theory, are an essential conceptual backbone in the formulation of quantum field theories capable of describing the world of elementary particles. This primer is an introduction to and survey of the underlying concepts and structures needed in order to understand and handle these powerful tools. Specifically, in Part I of the book the symmetries and related group theoretical structures of the Minkowskian space-time manifold are analyzed, while Part II examines the internal symmetries and their related unitary groups, where the interactions between fundamental particles are encoded as we know them from the present standard model of particle physics. This book, based on several courses given by the authors, addresses advanced graduate students and non-specialist researchers wishing to enter active research in the field, and having a working knowledge of classical field theory and relativistic quantum mechanics. Numerous end-of-chapter problems and their solutions will facilitate the use of this book as self-study guide or as course book for topical lectures.

Lorentz Group, CPT and Neutrinos

Andrew E. Chubykalo
Lorentz Group CPT and Neutrinos Book PDF

Author : Andrew E. Chubykalo
Publisher : World Scientific
Page : 492 pages
File Size : 40,9 Mb
Release : 2000
Category : Science
ISBN : 9810240627

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Lorentz Group, CPT and Neutrinos by Andrew E. Chubykalo Pdf

The topics in this volume range from mathematical aspects of the theory of the Poincar‚ group, Clifford algebras and the CPT theorem, through new theoretical physical constructions and concepts (such as the physical significance of the 4-potential, the interplay between quantum mechanics and gravity, Majorana-like models, the photon as a composite particle, action-at-a-distance and superluminal phenomena), to experiments in neutrino physics. The book will be of interest to graduate students and researchers working in fundamental physics and phenomenology, and also to experimentalists.