Physics Of The Lorentz Group

Author : Sibel Baskal,Young S Kim,Marilyn E Noz
Publisher : Morgan & Claypool Publishers
Page : 125 pages
File Size : 51,5 Mb
Release : 2015-11-01
Category : Science
ISBN : 9781681740621

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Physics of the Lorentz Group by Sibel Baskal,Young S Kim,Marilyn E Noz Pdf

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.

Author : Sibel Baskal,Young S Kim,Marilyn E Noz
Publisher : Morgan & Claypool Publishers
Page : 138 pages
File Size : 51,6 Mb
Release : 2015-11-01
Category : Science
ISBN : 9781681742540

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Physics of the Lorentz Group by Sibel Baskal,Young S Kim,Marilyn E Noz Pdf

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.

Author : Sibel Baskal,Y. S. Kim,Marilyn E. Noz
Publisher : Unknown
Page : 128 pages
File Size : 55,6 Mb
Release : 2021
Category : Lorentz groups
ISBN : 7560395228

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Physics of the Lorentz Group by Sibel Baskal,Y. S. Kim,Marilyn E. Noz Pdf

Author : Y S Kim
Publisher : Myprint
Page : 140 pages
File Size : 55,6 Mb
Release : 2015-11-17
Category : Electronic
ISBN : 1681748282

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Physics of the Lorentz Group by Y S Kim Pdf

Author : K. Srinivasa Rao
Publisher : John Wiley & Sons
Page : 380 pages
File Size : 43,9 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.

Author : Young Suh Kim,M. Noz
Publisher : Springer Science & Business Media
Page : 346 pages
File Size : 45,9 Mb
Release : 2012-12-06
Category : Science
ISBN : 9789400945586

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Theory and Applications of the Poincaré Group by Young Suh Kim,M. Noz Pdf

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.

Author : SIBEL. KIM BASKAL (YOUNG S. NOZ, MARILYN E.),Young S. Kim,Marilyn E. Noz
Publisher : IOP Publishing Limited
Page : 200 pages
File Size : 42,8 Mb
Release : 2021-05-26
Category : Mathematics
ISBN : 0750336056

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Physics of Lorentz Group Second Editiohb by SIBEL. KIM BASKAL (YOUNG S. NOZ, MARILYN E.),Young S. Kim,Marilyn E. Noz Pdf

This book explains the Lorentz group in a language familiar to physicists, namely in terms of two-by-two matrices. While the three-dimensional rotation group is one of the standard mathematical tools in physics, the Lorentz group applicable to the four-dimensional Minkowski space is still very strange to most physicists. However, it plays an essential role in a wide swathe of physics and is becoming the essential language for modern and rapidly developing fields. The first edition was primarily based on applications in high-energy physics developed during the latter half of the 20th Century, and the application of the same set of mathematical tools to optical sciences. In this new edition, the authors have added five new chapters to deal with emerging new problems in physics, such as quantum optics, information theory, and fundamental issues in physics including the question of whether quantum mechanics and special relativity are consistent with each other, or whether these two disciplines can be derived from the same set of equations. Key features Mathematical tools for all branches of physics Mathematics expressed in a language for physicists Focus on applications across physics disciplines Significantly extended new edition to include applications in modern areas of research

Author : I. M. Gelfand,R. A. Minlos,Z. Ya. Shapiro
Publisher : Courier Dover Publications
Page : 385 pages
File Size : 55,7 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.

Author : Roman U. Sexl,Helmuth K. Urbantke
Publisher : Springer Science & Business Media
Page : 388 pages
File Size : 54,5 Mb
Release : 2012-12-06
Category : Science
ISBN : 9783709162347

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Relativity, Groups, Particles by Roman U. Sexl,Helmuth K. Urbantke Pdf

This textbook bridges the gap between the level of introductory courses on mechanics and electrodynamics and the level of application in high energy physics and quantum field theory. After explaining the postulates that lead to the Lorentz transformation and after going through the main points special relativity has to make in classical mechanics and electrodynamics, the authors gradually lead the reader up to a more abstract point of view on relativistic symmetry - illustrated by physical examples - until finally motivating and developing Wigner's classification of the unitary irreducible representations of the inhomogeneous Lorentz group. Numerous historical and mathematical asides contribute to the conceptual clarification.

Author : M. Noz,Young Suh Kim
Publisher : Springer Science & Business Media
Page : 510 pages
File Size : 46,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9789400930513

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Special Relativity and Quantum Theory by M. Noz,Young Suh Kim Pdf

Special relativity and quantum mechanics are likely to remain the two most important languages in physics for many years to come. The underlying language for both disciplines is group theory. Eugene P. Wigner's 1939 paper on the Unitary Representations of the Inhomogeneous Lorentz Group laid the foundation for unifying the concepts and algorithms of quantum mechanics and special relativity. In view of the strong current interest in the space-time symmetries of elementary particles, it is safe to say that Wigner's 1939 paper was fifty years ahead of its time. This edited volume consists of Wigner's 1939 paper and the major papers on the Lorentz group published since 1939. . This volume is intended for graduate and advanced undergraduate students in physics and mathematics, as well as mature physicists wishing to understand the more fundamental aspects of physics than are available from the fashion-oriented theoretical models which come and go. The original papers contained in this volume are useful as supplementary reading material for students in courses on group theory, relativistic quantum mechanics and quantum field theory, relativistic electrodynamics, general relativity, and elementary particle physics. This reprint collection is an extension of the textbook by the present editors entitled "Theory and Applications of the Poincare Group." Since this book is largely based on the articles contained herein, the present volume should be viewed as a reading for the previous work. continuation of and supplementary We would like to thank Professors J. Bjorken, R. Feynman, R. Hofstadter, J.

Author : Werner Ruhl,Werner Rühl
Publisher : Unknown
Page : 326 pages
File Size : 42,9 Mb
Release : 1970
Category : Mathematics
ISBN : UVA:X001450474

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The Lorentz Group and Harmonic Analysis by Werner Ruhl,Werner Rühl Pdf

Author : M. A. Naimark
Publisher : Elsevier
Page : 465 pages
File Size : 52,6 Mb
Release : 2014-07-15
Category : Mathematics
ISBN : 9781483184982

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Linear Representations of the Lorentz Group by M. A. Naimark Pdf

Linear Representations of the Lorentz Group is a systematic exposition of the theory of linear representations of the proper Lorentz group and the complete Lorentz group. This book consists of four chapters. The first two chapters deal with the basic material on the three-dimensional rotation group, on the complete Lorentz group and the proper Lorentz group, as well as the theory of representations of the three-dimensional rotation group. These chapters also provide the necessary basic information from the general theory of group representations. The third chapter is devoted to the representations of the proper Lorentz group and the complete Lorentz group, while the fourth chapter examines the theory of invariant equations. This book will prove useful to mathematicians and students.

Author : Moshe Carmeli
Publisher : World Scientific
Page : 416 pages
File Size : 42,8 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.

Author : Jong-Ping Hsu,Yuan-Zhong Zhang
Publisher : World Scientific
Page : 620 pages
File Size : 44,8 Mb
Release : 2001
Category : Science
ISBN : 9812810986

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Lorentz and Poincar‚ Invariance by Jong-Ping Hsu,Yuan-Zhong Zhang Pdf

This collection of papers provides a broad view of the development of Lorentz and Poincar(r) invariance and spacetime symmetry throughout the past 100 years. The issues explored in these papers include: (1) formulations of relativity theories in which the speed of light is not a universal constant but which are consistent with the four-dimensional symmetry of the Lorentz and Poincar(r) groups and with experimental results, (2) analyses and discussions by Reichenbach concerning the concepts of simultaneity and physical time from a philosophical point of view, and (3) results achieved by the union of the relativity and quantum theories, marking the beginnings of quantum electrodynamics and relativistic quantum mechanics. Ten of the fundamental experiments testing special relativity are also discussed, showing that they actually support a four-dimensional spacetime based on broad Lorentz and Poincar(r) invariance which is more general than and includes the special theory of relativity. The generalization of the concepts of simultaneity, physical time and the nature of the speed of light within a four-dimensional spacetime framework leads to the conclusion that the symmetries embodied by the special theory of relativity can be realized using only a single postulate OCo the principle of relativity for physical laws. Contents: Theoretical Implications of Lorentz and Poincar(r) Invariance: The Dawn of Lorentz and Poincar(r) Invariance (1887OCo1905): Inquiries Regarding the Constancy of the Speed of Light (1908-1910); The Splendid Union of Special Relativity and Quantum Mechanics (1927OCo1949); The Isotropy of the Speed of Light c: A Convenient Assumption (1963OCo1995); The Logically Simplest Theory of Relativity and Its 4-Dimensional Symmetry (1990OCo1994); Experiments for Lorentz and Poincar(r) Invariance: The Fizeau Experiment; The WilsonOCoWilson Experiment; The Observation of the Muon Lifetime Dilation; The MassOCoVelocity Relation Experiment; The Thomas Precession Experiment; and other papers. Readership: Upper-level undergraduates, graduate students, researchers and academics in mathematical physics and theoretical physics."

Author : Giovanni Costa,Gianluigi Fogli
Publisher : Springer
Page : 291 pages
File Size : 55,9 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.