Wigner's Analysis of the Unitary Representations of the Poincaré Group
Author: Francis R. Halpern
Publisher:
Published: 1965
Total Pages: 70
ISBN-13:
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Unitary Representations of the Poincar Group and Relativistic Wave Equations
Author: Yoshio Ohnuki
Publisher: World Scientific
Published: 1988
Total Pages: 234
ISBN-13: 9789971502508
DOWNLOAD EBOOKThis 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.
Theory and Applications of the Poincaré Group
Author: Young Suh Kim
Publisher: Springer Science & Business Media
Published: 2012-12-06
Total Pages: 346
ISBN-13: 9400945582
DOWNLOAD EBOOKSpecial 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.
Unitary Representations of Reductive Lie Groups. (AM-118), Volume 118
Author: David A. Vogan Jr.
Publisher: Princeton University Press
Published: 2016-03-02
Total Pages: 320
ISBN-13: 1400882389
DOWNLOAD EBOOKThis book is an expanded version of the Hermann Weyl Lectures given at the Institute for Advanced Study in January 1986. It outlines some of what is now known about irreducible unitary representations of real reductive groups, providing fairly complete definitions and references, and sketches (at least) of most proofs. The first half of the book is devoted to the three more or less understood constructions of such representations: parabolic induction, complementary series, and cohomological parabolic induction. This culminates in the description of all irreducible unitary representation of the general linear groups. For other groups, one expects to need a new construction, giving "unipotent representations." The latter half of the book explains the evidence for that expectation and suggests a partial definition of unipotent representations.
Nuclear Science Abstracts
Author:
Publisher:
Published: 1971-10
Total Pages: 1644
ISBN-13:
DOWNLOAD EBOOKGeneral Relativity
Author: Robert M. Wald
Publisher: University of Chicago Press
Published: 2010-05-15
Total Pages: 507
ISBN-13: 0226870375
DOWNLOAD EBOOK"Wald's book is clearly the first textbook on general relativity with a totally modern point of view; and it succeeds very well where others are only partially successful. The book includes full discussions of many problems of current interest which are not treated in any extant book, and all these matters are considered with perception and understanding."—S. Chandrasekhar "A tour de force: lucid, straightforward, mathematically rigorous, exacting in the analysis of the theory in its physical aspect."—L. P. Hughston, Times Higher Education Supplement "Truly excellent. . . . A sophisticated text of manageable size that will probably be read by every student of relativity, astrophysics, and field theory for years to come."—James W. York, Physics Today
Phase Space Picture Of Quantum Mechanics: Group Theoretical Approach
Author: Young Suh Kim
Publisher: World Scientific
Published: 1991-03-06
Total Pages: 352
ISBN-13: 9814506672
DOWNLOAD EBOOKThis book covers the theory and applications of the Wigner phase space distribution function and its symmetry properties. The book explains why the phase space picture of quantum mechanics is needed, in addition to the conventional Schrödinger or Heisenberg picture. It is shown that the uncertainty relation can be represented more accurately in this picture. In addition, the phase space picture is shown to be the natural representation of quantum mechanics for modern optics and relativistic quantum mechanics of extended objects.
Theory of Group Representations and Applications
Author: Asim Orhan Barut
Publisher: World Scientific
Published: 1986
Total Pages: 750
ISBN-13: 9789971502171
DOWNLOAD EBOOKLie!algebras - Topological!groups - Lie!groups - Representations - Special!functions - Induced!representations.
Representations of *-Algebras, Locally Compact Groups, and Banach *-Algebraic Bundles
Author: J. M.G. Fell
Publisher: Academic Press
Published: 1988-05-01
Total Pages: 755
ISBN-13: 0080874452
DOWNLOAD EBOOKThis 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.
Springer Handbook of Spacetime
Author: Abhay Ashtekar
Publisher: Springer
Published: 2014-09-01
Total Pages: 883
ISBN-13: 3642419925
DOWNLOAD EBOOKThe Springer Handbook of Spacetime is dedicated to the ground-breaking paradigm shifts embodied in the two relativity theories, and describes in detail the profound reshaping of physical sciences they ushered in. It includes in a single volume chapters on foundations, on the underlying mathematics, on physical and astrophysical implications, experimental evidence and cosmological predictions, as well as chapters on efforts to unify general relativity and quantum physics. The Handbook can be used as a desk reference by researchers in a wide variety of fields, not only by specialists in relativity but also by researchers in related areas that either grew out of, or are deeply influenced by, the two relativity theories: cosmology, astronomy and astrophysics, high energy physics, quantum field theory, mathematics, and philosophy of science. It should also serve as a valuable resource for graduate students and young researchers entering these areas, and for instructors who teach courses on these subjects. The Handbook is divided into six parts. Part A: Introduction to Spacetime Structure. Part B: Foundational Issues. Part C: Spacetime Structure and Mathematics. Part D: Confronting Relativity theories with observations. Part E: General relativity and the universe. Part F: Spacetime beyond Einstein.
