Physics Of Lorentz Group Second Editiohb

Author : SIBEL. KIM BASKAL (YOUNG S. NOZ, MARILYN E.),Young S. Kim,Marilyn E. Noz
Publisher : IOP Publishing Limited
Page : 200 pages
File Size : 42,6 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 : Sibel Baskal,Young S Kim,Marilyn E Noz
Publisher : Morgan & Claypool Publishers
Page : 125 pages
File Size : 45,5 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 : K. I. M. BASKAL
Publisher : Unknown
Page : 128 pages
File Size : 53,6 Mb
Release : 2021-05-31
Category : Electronic
ISBN : 0750336080

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Physics of Lorentz Group Second Editio by K. I. M. BASKAL Pdf

Author : I. M. Gelfand,R. A. Minlos,Z. Ya. Shapiro
Publisher : Courier Dover Publications
Page : 385 pages
File Size : 47,5 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 : H.F Jones
Publisher : CRC Press
Page : 348 pages
File Size : 51,8 Mb
Release : 2020-07-14
Category : Mathematics
ISBN : 142005029X

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Groups, Representations and Physics by H.F Jones Pdf

Illustrating the fascinating interplay between physics and mathematics, Groups, Representations and Physics, Second Edition provides a solid foundation in the theory of groups, particularly group representations. For this new, fully revised edition, the author has enhanced the book's usefulness and widened its appeal by adding a chapter on the Cartan-Dynkin treatment of Lie algebras. This treatment, a generalization of the method of raising and lowering operators used for the rotation group, leads to a systematic classification of Lie algebras and enables one to enumerate and construct their irreducible representations. Taking an approach that allows physics students to recognize the power and elegance of the abstract, axiomatic method, the book focuses on chapters that develop the formalism, followed by chapters that deal with the physical applications. It also illustrates formal mathematical definitions and proofs with numerous concrete examples.

Author : A E Chubykalo,Valeri V Dvoeglazov,David J Ernst,Vladimir G Kadyshevsky,Young Suh Kim
Publisher : World Scientific
Page : 486 pages
File Size : 54,8 Mb
Release : 2000-08-30
Category : Science
ISBN : 9789814543392

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Lorentz Group, Cpt And Neutrinos: Proceedings Of The International Workshop by A E Chubykalo,Valeri V Dvoeglazov,David J Ernst,Vladimir G Kadyshevsky,Young Suh Kim Pdf

The topics in this volume range from mathematical aspects of the theory of the Poincaré 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.

Author : Young Suh Kim,M. Noz
Publisher : Springer Science & Business Media
Page : 346 pages
File Size : 42,5 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 : Anonim
Publisher : Unknown
Page : 128 pages
File Size : 51,7 Mb
Release : 2024-07-01
Category : Electronic
ISBN : 9789814478649

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A Broader View of Relativity by Anonim Pdf

Author : Werner Ruhl,Werner Rühl
Publisher : Unknown
Page : 326 pages
File Size : 51,7 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 : Moshe Carmeli
Publisher : World Scientific
Page : 416 pages
File Size : 50,9 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 : Daniel S Nydick,K Thomas R Davies
Publisher : Unknown
Page : 170 pages
File Size : 55,9 Mb
Release : 2020-05-25
Category : Electronic
ISBN : 9798645762230

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From the Lorentz Transformation to the Dirac Equation by Daniel S Nydick,K Thomas R Davies Pdf

This book on Special Relativity, with unique chapters on the Dirac equation and General Relativity, is especially suitable for a one-semester undergraduate physics course on Special Relativity (with perhaps some coverage of the qualitative features of General Relativity). It can also be used in a combination of undergraduate courses including modern physics, particle physics, optics, and Quantum Mechanics; or in classical mechanics at the physics graduate level. The book also includes coverage of the history of relativity, particularly with respect to developments in electricity and magnetism, particle physics, and cosmology. This is the revised second edition.

Author : Gregory L. Naber
Publisher : Springer Science & Business Media
Page : 336 pages
File Size : 51,5 Mb
Release : 2012-02-02
Category : Mathematics
ISBN : 9781441978387

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The Geometry of Minkowski Spacetime by Gregory L. Naber Pdf

This book offers a presentation of the special theory of relativity that is mathematically rigorous and yet spells out in considerable detail the physical significance of the mathematics. It treats, in addition to the usual menu of topics one is accustomed to finding in introductions to special relativity, a wide variety of results of more contemporary origin. These include Zeeman’s characterization of the causal automorphisms of Minkowski spacetime, the Penrose theorem on the apparent shape of a relativistically moving sphere, a detailed introduction to the theory of spinors, a Petrov-type classification of electromagnetic fields in both tensor and spinor form, a topology for Minkowski spacetime whose homeomorphism group is essentially the Lorentz group, and a careful discussion of Dirac’s famous Scissors Problem and its relation to the notion of a two-valued representation of the Lorentz group. This second edition includes a new chapter on the de Sitter universe which is intended to serve two purposes. The first is to provide a gentle prologue to the steps one must take to move beyond special relativity and adapt to the presence of gravitational fields that cannot be considered negligible. The second is to understand some of the basic features of a model of the empty universe that differs markedly from Minkowski spacetime, but may be recommended by recent astronomical observations suggesting that the expansion of our own universe is accelerating rather than slowing down. The treatment presumes only a knowledge of linear algebra in the first three chapters, a bit of real analysis in the fourth and, in two appendices, some elementary point-set topology. The first edition of the book received the 1993 CHOICE award for Outstanding Academic Title. Reviews of first edition: “... a valuable contribution to the pedagogical literature which will be enjoyed by all who delight in precise mathematics and physics.” (American Mathematical Society, 1993) “Where many physics texts explain physical phenomena by means of mathematical models, here a rigorous and detailed mathematical development is accompanied by precise physical interpretations.” (CHOICE, 1993) “... his talent in choosing the most significant results and ordering them within the book can’t be denied. The reading of the book is, really, a pleasure.” (Dutch Mathematical Society, 1993)

Author : Jakob Schwichtenberg
Publisher : Springer
Page : 287 pages
File Size : 41,6 Mb
Release : 2017-12-01
Category : Science
ISBN : 9783319666310

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Physics from Symmetry by Jakob Schwichtenberg Pdf

This is a textbook that derives the fundamental theories of physics from symmetry. It starts by introducing, in a completely self-contained way, all mathematical tools needed to use symmetry ideas in physics. Thereafter, these tools are put into action and by using symmetry constraints, the fundamental equations of Quantum Mechanics, Quantum Field Theory, Electromagnetism, and Classical Mechanics are derived. As a result, the reader is able to understand the basic assumptions behind, and the connections between the modern theories of physics. The book concludes with first applications of the previously derived equations. Thanks to the input of readers from around the world, this second edition has been purged of typographical errors and also contains several revised sections with improved explanations.

Author : Roman U. Sexl,Helmuth K. Urbantke
Publisher : Springer Science & Business Media
Page : 388 pages
File Size : 47,8 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 : Jong-Ping Hsu,Leonardo Hsu
Publisher : World Scientific
Page : 538 pages
File Size : 53,6 Mb
Release : 2006
Category : Science
ISBN : 9789812566515

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A Broader View of Relativity by Jong-Ping Hsu,Leonardo Hsu Pdf

A Broader View of Relativity shows that there is still new life in old physics. The book examines the historical context and theoretical underpinnings of Einstein's theory of special relativity and describes Broad Relativity, a generalized theory of coordinate transformations between inertial reference frames that includes Einstein's special relativity as a special case. It shows how the principle of relativity is compatible with multiple concepts of physical time and these different procedures for clock synchronization can be useful for thinking about different physical problems, including many-body systems and the development of a Lorentz-invariant thermodynamics. Broad relativity also provides new answers to old questions such as the necessity of postulating the constancy of the speed of light and the viability of Reichenbach's general concept of time. The book also draws on the idea of limiting-four-dimensional symmetry to describe coordinate transformations and the physics of particles and fields in non-inertial frames, particularly those with constant linear accelerations. This new edition expands the discussion on the role that human conventions and unit systems have played in the historical development of relativity theories and includes new results on the implications of broad relativity for clarifying the status of constants that are truly fundamental and inherent properties of our universe. Contents: Special Relativity is NOT Incorrect!; Space, Time, and Inertial Frames; The Novel Creation of the Young Einstein; Experimental Tests; Group Properties; Common Relativity and Quantum Mechanics; Extended Relativity; Dynamics of Classical and Quantum Particles; Group and Lie Algebra Properties of Accelerated Transformation of Spacetime; Graphic Representations of the Geometry of Spacetime in Accelerated Frames; Two Rocketships with Constant-Linear Acceleration; On a Gauge Theory of Gravity with Translation Gauge Symmetry in Inertial and Non-Inertial Frames; Appendices: Technical Aspects of Extended Relativity; Coordinate Transformations for Rotating Frames; and other papers. Key Features Includes five new chapters A complete and comprehensive description of Broad Relativity, which generalizes Einstein's original theory of special relativity to new physical time systems and a limited class of non-inertial frames Brings a fresh viewpoint with new physical implications and predictions to old physics Gives an updated discussion on fundamental physical constants and unit systems and their influence on the development of relativity theories Readership: Researchers in the field of relativity theory and advanced undergraduate students as a supplementary text.