Linear Representatives Of The Lorentz Group
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| Author | : M. A. Naimark |
| Publisher | : Elsevier |
| Total Pages | : 465 |
| Release | : 2014-07-15 |
| Genre | : Mathematics |
| ISBN | : 1483184986 |
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 | : Nelson Dunford |
| Publisher | : John Wiley & Sons |
| Total Pages | : 1092 |
| Release | : 1988-02-23 |
| Genre | : Mathematics |
| ISBN | : 0471608475 |
This classic text, written by two notable mathematicians, constitutes a comprehensive survey of the general theory of linear operations, together with applications to the diverse fields of more classical analysis. Dunford and Schwartz emphasize the significance of the relationships between the abstract theory and its applications. This text has been written for the student as well as for the mathematician—treatment is relatively self-contained. This is a paperback edition of the original work, unabridged, in three volumes.
| Author | : K. Srinivasa Rao |
| Publisher | : John Wiley & Sons |
| Total Pages | : 380 |
| Release | : 1988 |
| Genre | : Business & Economics |
| ISBN | : 9780470210444 |
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 |
| Total Pages | : 173 |
| Release | : 2015-11-01 |
| Genre | : Science |
| ISBN | : 1681740621 |
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 | : I. M. Gelfand |
| Publisher | : Courier Dover Publications |
| Total Pages | : 385 |
| Release | : 2018-04-18 |
| Genre | : Science |
| ISBN | : 0486823857 |
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 | : Werner Ruhl |
| Publisher | : |
| Total Pages | : 326 |
| Release | : 1970 |
| Genre | : Mathematics |
| ISBN | : |
| Author | : Andrew M. Steane |
| Publisher | : Oxford University Press |
| Total Pages | : 437 |
| Release | : 2012-10-04 |
| Genre | : Science |
| ISBN | : 019966286X |
This book unfolds the subject of Relativity for undergraduate students of physics. It is intended to allow an undergraduate physics course to extend somewhat further and wider in this area than has traditionally been the case, while ensuring that the mainstream of students can handle the material. Introducing Lorentz invariants and four-vectors early on, but postponing tensor notation till it is needed, the aim is to make manageable what would otherwise beregarded as hard; to make derivations as simple as possible and physical ideas as transparent as possible.
| Author | : Pertti Lounesto |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 664 |
| Release | : 2004 |
| Genre | : Mathematics |
| ISBN | : 9780817635251 |
In addition, attention is paid to the algebraic and Lie-theoretic applications of Clifford algebras---particularly their intersection with Hopf algebras, Lie algebras and representations, graded algebras, and associated mathematical structures. Symplectic Clifford algebras are also discussed. Finally, Clifford algebras play a strong role in both physics and engineering. The physics section features an investigation of geometric algebras, chiral Dirac equations, spinors and Fermions, and applications of Clifford algebras in classical mechanics and general relativity. Twistor and octonionic methods, electromagnetism and gravity, elementary particle physics, noncommutative physics, Dirac's equation, quantum spheres, and the Standard Model are among topics considered at length.
| Author | : Graham S Hall |
| Publisher | : World Scientific |
| Total Pages | : 443 |
| Release | : 2004-04-27 |
| Genre | : Science |
| ISBN | : 9814505315 |
This is a text on classical general relativity from a geometrical viewpoint. Introductory chapters are provided on algebra, topology and manifold theory, together with a chapter on the basic ideas of space-time manifolds and Einstein's theory. There is a detailed account of algebraic structures and tensor classification in general relativity and also of the relationships between the metric, connection and curvature structures on space-times. The latter includes chapters on holonomy and sectional curvature. An extensive study is presented of symmetries in general relativity, including isometries, homotheties, conformal symmetries and affine, projective and curvature collineations. Several general properties of such symmetries are studied and a preparatory section on transformation groups and on the properties of Lie algebras of vector fields on manifolds is provided.
| Author | : |
| Publisher | : Academic Press |
| Total Pages | : 445 |
| Release | : 1973-03-02 |
| Genre | : Mathematics |
| ISBN | : 0080873650 |
Symmetry Groups and Their Applications
