Theory and Applications of the Poincaré Group
Theory and Applications of the Poincaré Group

Author: Young Suh Kim

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 346

ISBN-13: 9400945582

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Special relativity and quantum mechanics, formulated early in the twentieth century, are the two most important scientific languages and are likely to remain so for many years to come. In the 1920's, when quantum mechanics was developed, the most pressing theoretical problem was how to make it consistent with special relativity. In the 1980's, this is still the most pressing problem. The only difference is that the situation is more urgent now than before, because of the significant quantity of experimental data which need to be explained in terms of both quantum mechanics and special relativity. In unifying the concepts and algorithms of quantum mechanics and special relativity, it is important to realize that the underlying scientific language for both disciplines is that of group theory. The role of group theory in quantum mechanics is well known. The same is true for special relativity. Therefore, the most effective approach to the problem of unifying these two important theories is to develop a group theory which can accommodate both special relativity and quantum mechanics. As is well known, Eugene P. Wigner is one of the pioneers in developing group theoretical approaches to relativistic quantum mechanics. His 1939 paper on the inhomogeneous Lorentz group laid the foundation for this important research line. It is generally agreed that this paper was somewhat ahead of its time in 1939, and that contemporary physicists must continue to make real efforts to appreciate fully the content of this classic work.

Physics of the Lorentz Group
Physics of the Lorentz Group

Author: Sibel Baskal

Publisher: Morgan & Claypool Publishers

Published: 2015-11-01

Total Pages: 173

ISBN-13: 1681740621

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This book explains the Lorentz mathematical group in a language familiar to physicists. While the three-dimensional rotation group is one of the standard mathematical tools in physics, the Lorentz group of the four-dimensional Minkowski space is still very strange to most present-day physicists. It plays an essential role in understanding particles moving at close to light speed and is becoming the essential language for quantum optics, classical optics, and information science. The book is based on papers and books published by the authors on the representations of the Lorentz group based on harmonic oscillators and their applications to high-energy physics and to Wigner functions applicable to quantum optics. It also covers the two-by-two representations of the Lorentz group applicable to ray optics, including cavity, multilayer and lens optics, as well as representations of the Lorentz group applicable to Stokes parameters and the Poincaré sphere on polarization optics.

Massless Representations of the Poincaré Group
Massless Representations of the Poincaré Group

Author: R. Mirman

Publisher: iUniverse

Published: 2005-05

Total Pages: 233

ISBN-13: 0595341241

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Preface 1 The Physical Meaning of Poincare Massless Representations 1 2 Massless Representations 12 3 Massless Fields are Different 32 4 How to Couple Massless and Massive Matter 56 5 The Behavior of Matter in Fields 73 6 Geometrical Reasons for the Poincare Group 95 7 Description of the Electromagnetic Field 123 8 The Equations Governing Free Gravitation 135 9 How Matter Determines Gravitational Fields 150 10 Nonlinearity and Geometry 165 11 Quantum Gravity 183 References 201 Index 207.

Unitary Representations of the Poincar‚ Group and Relativistic Wave Equations
Unitary Representations of the Poincar‚ Group and Relativistic Wave Equations

Author: Yoshio Ohnuki

Publisher: World Scientific

Published: 1988

Total Pages: 234

ISBN-13: 9789971502508

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This book is devoted to an extensive and systematic study on unitary representations of the Poincar‚ group. The Poincar‚ group plays an important role in understanding the relativistic picture of particles in quantum mechanics. Complete knowledge of every free particle states and their behaviour can be obtained once all the unitary irreducible representations of the Poincar‚ group are found. It is a surprising fact that a simple framework such as the Poincar‚ group, when unified with quantum theory, fixes our possible picture of particles severely and without exception. In this connection, the theory of unitary representations of the Poincar‚ group provides a fundamental concept of relativistic quantum mechanics and field theory.

Group Theory and General Relativity
Group Theory and General Relativity

Author: Moshe Carmeli

Publisher: World Scientific

Published: 2000

Total Pages: 416

ISBN-13: 9781860942341

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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.

Linear Differential Equations and Group Theory from Riemann to Poincare
Linear Differential Equations and Group Theory from Riemann to Poincare

Author: Jeremy Gray

Publisher: Springer Science & Business Media

Published: 2010-01-07

Total Pages: 357

ISBN-13: 0817647732

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This book is a study of how a particular vision of the unity of mathematics, often called geometric function theory, was created in the 19th century. The central focus is on the convergence of three mathematical topics: the hypergeometric and related linear differential equations, group theory, and on-Euclidean geometry. The text for this second edition has been greatly expanded and revised, and the existing appendices enriched. The exercises have been retained, making it possible to use the book as a companion to mathematics courses at the graduate level.

Group Theory in a Nutshell for Physicists
Group Theory in a Nutshell for Physicists

Author: A. Zee

Publisher: Princeton University Press

Published: 2016-03-29

Total Pages: 632

ISBN-13: 1400881188

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A concise, modern textbook on group theory written especially for physicists Although group theory is a mathematical subject, it is indispensable to many areas of modern theoretical physics, from atomic physics to condensed matter physics, particle physics to string theory. In particular, it is essential for an understanding of the fundamental forces. Yet until now, what has been missing is a modern, accessible, and self-contained textbook on the subject written especially for physicists. Group Theory in a Nutshell for Physicists fills this gap, providing a user-friendly and classroom-tested text that focuses on those aspects of group theory physicists most need to know. From the basic intuitive notion of a group, A. Zee takes readers all the way up to how theories based on gauge groups could unify three of the four fundamental forces. He also includes a concise review of the linear algebra needed for group theory, making the book ideal for self-study. Provides physicists with a modern and accessible introduction to group theory Covers applications to various areas of physics, including field theory, particle physics, relativity, and much more Topics include finite group and character tables; real, pseudoreal, and complex representations; Weyl, Dirac, and Majorana equations; the expanding universe and group theory; grand unification; and much more The essential textbook for students and an invaluable resource for researchers Features a brief, self-contained treatment of linear algebra An online illustration package is available to professors Solutions manual (available only to professors)

Symmetries and Group Theory in Particle Physics
Symmetries and Group Theory in Particle Physics

Author: Giovanni Costa

Publisher: Springer

Published: 2012-02-03

Total Pages: 300

ISBN-13: 3642154824

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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.

Group Theory in Physics
Group Theory in Physics

Author: Wu-Ki Tung

Publisher: World Scientific

Published: 1985

Total Pages: 368

ISBN-13: 9971966565

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An introductory text book for graduates and advanced undergraduates on group representation theory. It emphasizes group theory's role as the mathematical framework for describing symmetry properties of classical and quantum mechanical systems. Familiarity with basic group concepts and techniques is invaluable in the education of a modern-day physicist. This book emphasizes general features and methods which demonstrate the power of the group-theoretical approach in exposing the systematics of physical systems with associated symmetry. Particular attention is given to pedagogy. In developing the theory, clarity in presenting the main ideas and consequences is given the same priority as comprehensiveness and strict rigor. To preserve the integrity of the mathematics, enough technical information is included in the appendices to make the book almost self-contained. A set of problems and solutions has been published in a separate booklet.