[PDF] Linear Representations Of The Lorentz Group eBook

Author : M. A. Naimark
Publisher : Elsevier
Page : 465 pages
File Size : 20,60 MB
Release : 2014-07-15
Category : Mathematics
ISBN : 1483184986

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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 : I. M. Gelfand
Publisher : Courier Dover Publications
Page : 385 pages
File Size : 40,10 MB
Release : 2018-04-18
Category : Science
ISBN : 0486823857

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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 : K. Srinivasa Rao
Publisher : John Wiley & Sons
Page : 380 pages
File Size : 46,33 MB
Release : 1988
Category : Business & Economics
ISBN : 9780470210444

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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 : Sibel Baskal
Publisher : Morgan & Claypool Publishers
Page : 173 pages
File Size : 20,10 MB
Release : 2015-11-01
Category : Science
ISBN : 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.