Representations Of The Rotation And Lorentz Groups And Their Applications
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Representations Of The Rotation And Lorentz Groups And Their Applications
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Author : I. M. Gelfand
language : en
Publisher: Courier Dover Publications
Release Date : 2018-04-18
Representations Of The Rotation And Lorentz Groups And Their Applications written by I. M. Gelfand and has been published by Courier Dover Publications this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-04-18 with Science categories.
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.
Physics Of The Lorentz Group
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Author : Sibel Baskal
language : en
Publisher: Morgan & Claypool Publishers
Release Date : 2015-11-01
Physics Of The Lorentz Group written by Sibel Baskal and has been published by Morgan & Claypool Publishers this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-11-01 with Science categories.
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.
Group Theory And General Relativity
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Author : Moshe Carmeli
language : en
Publisher: World Scientific
Release Date : 2000
Group Theory And General Relativity written by Moshe Carmeli and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with Science categories.
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.
Representations Of The Rotation And Lorentz Groups And Their Applications
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Author : Izrailʹ Moiseevich Gelʹfand
language : en
Publisher:
Release Date : 1963
Representations Of The Rotation And Lorentz Groups And Their Applications written by Izrailʹ Moiseevich Gelʹfand and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1963 with Group theory categories.
Applications Of Group Theory In Quantum Mechanics
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Author : M. I. Petrashen
language : en
Publisher: Courier Corporation
Release Date : 2013-01-03
Applications Of Group Theory In Quantum Mechanics written by M. I. Petrashen and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-01-03 with Science categories.
Geared toward postgraduate students, theoretical physicists, and researchers, this advanced text explores the role of modern group-theoretical methods in quantum theory. The authors based their text on a physics course they taught at a prominent Soviet university. Readers will find it a lucid guide to group theory and matrix representations that develops concepts to the level required for applications. The text's main focus rests upon point and space groups, with applications to electronic and vibrational states. Additional topics include continuous rotation groups, permutation groups, and Lorentz groups. A number of problems involve studies of the symmetry properties of the Schroedinger wave function, as well as the explanation of "additional" degeneracy in the Coulomb field and certain subjects in solid-state physics. The text concludes with an instructive account of problems related to the conditions for relativistic invariance in quantum theory.
Technical Report Jet Propulsion Laboratory California Institute Of Technology
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Author : Jet Propulsion Laboratory (U.S.)
language : en
Publisher:
Release Date :
Technical Report Jet Propulsion Laboratory California Institute Of Technology written by Jet Propulsion Laboratory (U.S.) and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on with Jet propulsion categories.
Unitary Representations Of The Poincar Group And Relativistic Wave Equations
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Author : Yoshio Ohnuki
language : en
Publisher: World Scientific
Release Date : 1988
Unitary Representations Of The Poincar Group And Relativistic Wave Equations written by Yoshio Ohnuki and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1988 with Science categories.
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.
Integral Geometry And Representation Theory
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Author : I. M. Gel'fand
language : en
Publisher: Academic Press
Release Date : 2014-05-12
Integral Geometry And Representation Theory written by I. M. Gel'fand and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-12 with Mathematics categories.
Generalized Functions, Volume 5: Integral Geometry and Representation Theory is devoted to the theory of representations, focusing on the group of two-dimensional complex matrices of determinant one. This book emphasizes that the theory of representations is a good example of the use of algebraic and geometric methods in functional analysis, in which transformations are performed not on the points of a space, but on the functions defined on it. The topics discussed include Radon transform on a real affine space, integral transforms in the complex domain, and representations of the group of complex unimodular matrices in two dimensions. The properties of the Fourier transform on G, integral geometry in a space of constant curvature, harmonic analysis on spaces homogeneous with respect to the Lorentz Group, and invariance under translation and dilation are also described. This volume is suitable for mathematicians, specialists, and students learning integral geometry and representation theory.
Representations Of Algebras Locally Compact Groups And Banach Algebraic Bundles
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Author : J. M.G. Fell
language : en
Publisher: Academic Press
Release Date : 1988-04-15
Representations Of Algebras Locally Compact Groups And Banach Algebraic Bundles written by J. M.G. Fell and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1988-04-15 with Mathematics categories.
This is an all-encompassing and exhaustive exposition of the theory of infinite-dimensional Unitary Representations of Locally Compact Groups and its generalization to representations of Banach algebras. The presentation is detailed, accessible, and self-contained (except for some elementary knowledge in algebra, topology, and abstract measure theory). In the later chapters the reader is brought to the frontiers of present-day knowledge in the area of Mackey normal subgroup analysisand its generalization to the context of Banach *-Algebraic Bundles.
Compact Lie Groups And Their Representations
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Author : Dmitriĭ Petrovich Zhelobenko
language : en
Publisher: American Mathematical Soc.
Release Date : 1973-01-01
Compact Lie Groups And Their Representations written by Dmitriĭ Petrovich Zhelobenko and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1973-01-01 with Mathematics categories.