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Reduction Of The Direct Product Of Representations Of The Poincare Group
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Book Synopsis Reduction of the Direct Product of Representations of the Poincareʹ Group by : H. E. Moses
Download or read book Reduction of the Direct Product of Representations of the Poincareʹ Group written by H. E. Moses and published by . This book was released on 1969 with total page 52 pages. Available in PDF, EPUB and Kindle. Book excerpt: The factors of the direct product and the representations which appear in the expansion are expressed in terms of a particular momentum representation called 'the standard helicity representation' which enables one to use a uniform notation for all masses, whether real, zero, or imaginary. The earlier portions of the present paper summarizes the properties of these representations.
Book Synopsis Reduction of the Direct Product of Representations of the Poincareʹ Group by : H. E. Moses
Download or read book Reduction of the Direct Product of Representations of the Poincareʹ Group written by H. E. Moses and published by . This book was released on 1969 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: The direct product of two representations of the Poincare group are expanded into representations of the Poincare group in the general case that the factors of the direct product may have any mass, whether real, zero, or imaginary, and the total energy may be indefinite. The representations of the Poincare group, which appear in the expansion of the direct product have masses which run through a continuous spectrum of real and imaginary values and are irreducible in terms of the mass and sign of energy (for real mass), but are reducible in terms of the infinitesimal generators of the little groups. To obtain the expansion in terms of irreducible representations, one need only reduce the infinitesimal generators of the little groups. This reduction is carried out for the real mass components and, in principal at least, can be carried out for the infinitesimal generators for the imaginary mass components.
Book Synopsis Scientific and Technical Aerospace Reports by :
Download or read book Scientific and Technical Aerospace Reports written by and published by . This book was released on 1970 with total page 848 pages. Available in PDF, EPUB and Kindle. Book excerpt: Lists citations with abstracts for aerospace related reports obtained from world wide sources and announces documents that have recently been entered into the NASA Scientific and Technical Information Database.
Book Synopsis The Reduction of the Product of Two Irreducible Unitary Representations of the Proper Orthochronous Quantummechanical Poincaré Group by : Manfred Schaaf
Download or read book The Reduction of the Product of Two Irreducible Unitary Representations of the Proper Orthochronous Quantummechanical Poincaré Group written by Manfred Schaaf and published by Springer. This book was released on 1970 with total page 136 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Group Theory And Hopf Algebras: Lectures For Physicists by : Aiyalam P Balachandran
Download or read book Group Theory And Hopf Algebras: Lectures For Physicists written by Aiyalam P Balachandran and published by World Scientific. This book was released on 2010-07-22 with total page 270 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is addressed to graduate students and research workers in theoretical physics who want a thorough introduction to group theory and Hopf algebras. It is suitable for a one-semester course in group theory or a two-semester course which also treats advanced topics. Starting from basic definitions, it goes on to treat both finite and Lie groups as well as Hopf algebras. Because of the diversity in the choice of topics, which does not place undue emphasis on finite or Lie groups, it should be useful to physicists working in many branches.A unique aspect of the book is its treatment of Hopf algebras in a form accessible to physicists. Hopf algebras are generalizations of groups and their concepts are acquiring importance in the treatment of conformal field theories, noncommutative spacetimes, topological quantum computation and other important domains of investigation. But there is a scarcity of treatments of Hopf algebras at a level and in a manner that physicists are comfortable with. This book addresses this need superbly.There are illustrative examples from physics scattered throughout the book and in its set of problems. It also has a good bibliography. These features should enhance its value to readers.The authors are senior physicists with considerable research and teaching experience in diverse aspects of fundamental physics. The book, being the outcome of their combined efforts, stands testament to their knowledge and pedagogical skills.
Book Synopsis The Reduction of the Product of Two Irreductible Unitary Representations of the Proper Orthochronous Quantummechanical Poincare Group by : Manfred Schaaf
Download or read book The Reduction of the Product of Two Irreductible Unitary Representations of the Proper Orthochronous Quantummechanical Poincare Group written by Manfred Schaaf and published by . This book was released on 1970 with total page 120 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Nuclear Science Abstracts written by and published by . This book was released on 1974 with total page 596 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Il Nuovo cimento della Società italiana di fisica by :
Download or read book Il Nuovo cimento della Società italiana di fisica written by and published by . This book was released on 1980 with total page 1000 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Theory of Group Representations and Applications by : Asim Orhan Barut
Download or read book Theory of Group Representations and Applications written by Asim Orhan Barut and published by World Scientific. This book was released on 1986 with total page 750 pages. Available in PDF, EPUB and Kindle. Book excerpt: Lie!algebras - Topological!groups - Lie!groups - Representations - Special!functions - Induced!representations.
Book Synopsis Theory and Applications of the Poincaré Group by : Young Suh Kim
Download or read book Theory and Applications of the Poincaré Group written by Young Suh Kim and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 346 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Group Theoretical Foundations of Quantum Mechanics by : R. Mirman
Download or read book Group Theoretical Foundations of Quantum Mechanics written by R. Mirman and published by iUniverse. This book was released on 2005-05 with total page 281 pages. Available in PDF, EPUB and Kindle. Book excerpt: Table of Contents Preface 1 Foundations 1 2 Why Geometry, so Physics, Require Complex Numbers 25 3 Properties of Statefunctions 38 4 The Foundations of Coherent Superposition 58 5 Geometry, Transformations, Groups and Observers 85 6 The Poincare Group and Its Implications 108 7 The Dimension of Space 122 8 Bosons, Fermions, Spinors and Orthogonal Groups 146 9 The Complete Reasonableness of Quantum Mechanics 159 A: Terminology and Conventions 177 The Einstein Podolsky Rosen Paradox 185 Experimental Meaning of the Concept of Identical Particles 191 Nonexistence of Superselection Rules; Definition of Term "Frame of Reference" 203 Complex Groups, Quantum Mechanics, and the Dimension and Reality of Space 221 The Reality and Dimension of Space and the Complexity of Quantum Mechanics 235 References 255 Index 259.
Book Synopsis Theoretical and Mathematical Physics by :
Download or read book Theoretical and Mathematical Physics written by and published by . This book was released on 1983 with total page 680 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Bibliography, with Abstracts, of AFCRL Publications from 1 July to 30 September 1969 by : Air Force Cambridge Research Laboratories (U.S.)
Download or read book Bibliography, with Abstracts, of AFCRL Publications from 1 July to 30 September 1969 written by Air Force Cambridge Research Laboratories (U.S.) and published by . This book was released on 1969 with total page 110 pages. Available in PDF, EPUB and Kindle. Book excerpt: This bibliography lists all AFCRL in-house reports, journal articles, and contractor reports issued from 1 July to 30 September 1969. Abstracts are included for the in-house and contractor reports.
Book Synopsis Group Theory and Its Applications by : Ernest M. Loebl
Download or read book Group Theory and Its Applications written by Ernest M. Loebl and published by Academic Press. This book was released on 2014-05-12 with total page 725 pages. Available in PDF, EPUB and Kindle. Book excerpt: Group Theory and Its Applications focuses on the applications of group theory in physics and chemistry. The selection first offers information on the algebras of lie groups and their representations and induced and subduced representations. Discussions focus on the functions of positive type and compact groups; orthogonality relations for square-integrable representations; group, topological, Borel, and quotient structures; and classification of semisimple lie algebras in terms of their root systems. The text then takes a look at the generalization of Euler's angles and projective representation of the Poincare group in a quaternionic Hilbert space. The manuscript ponders on group theory in atomic spectroscopy, group lattices and homomorphism, and group theory in solid state physics. Topics include band theory of solids, lattice vibrations in solids, stationary states in the quantum theory of matter, coupled tensors, and shell structure. The text then examines the group theory of harmonic oscillators and nuclear structure and de Sitter space and positive energy. The selection is a dependable reference for physicists and chemists interested in group theory and its applications.
Book Synopsis Government Reports Annual Index by :
Download or read book Government Reports Annual Index written by and published by . This book was released on 1969 with total page 938 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Variations on a Theme by Kepler by : Victor Guillemin
Download or read book Variations on a Theme by Kepler written by Victor Guillemin and published by American Mathematical Soc.. This book was released on 1990 with total page 98 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is based on the Colloquium Lectures presented by Shlomo Sternberg in 1990. The authors delve into the mysterious role that groups, especially Lie groups, play in revealing the laws of nature by focusing on the familiar example of Kepler motion: the motion of a planet under the attraction of the sun according to Kepler's laws. Newton realized that Kepler's second law--that equal areas are swept out in equal times--has to do with the fact that the force is directed radially to the sun. Kepler's second law is really the assertion of the conservation of angular momentum, reflecting the rotational symmetry of the system about the origin of the force. In today's language, we would say that the group $O(3)$ (the orthogonal group in three dimensions) is responsible for Kepler's second law. By the end of the nineteenth century, the inverse square law of attraction was seen to have $O(4)$ symmetry (where $O(4)$ acts on a portion of the six-dimensional phase space of the planet). Even larger groups have since been found to be involved in Kepler motion. In quantum mechanics, the example of Kepler motion manifests itself as the hydrogen atom. Exploring this circle of ideas, the first part of the book was written with the general mathematical reader in mind. The remainder of the book is aimed at specialists. It begins with a demonstration that the Kepler problem and the hydrogen atom exhibit $O(4)$ symmetry and that the form of this symmetry determines the inverse square law in classical mechanics and the spectrum of the hydrogen atom in quantum mechanics. The space of regularized elliptical motions of the Kepler problem (also known as the Kepler manifold) plays a central role in this book. The last portion of the book studies the various cosmological models in this same conformal class (and having varying isometry groups) from the viewpoint of projective geometry. The computation of the hydrogen spectrum provides an illustration of the principle that enlarging the phase space can simplify the equations of motion in the classical setting and aid in the quantization problem in the quantum setting. The authors provide a short summary of the homological quantization of constraints and a list of recent applications to many interesting finite-dimensional settings. The book closes with an outline of Kostant's theory, in which a unitary representation is associated to the minimal nilpotent orbit of $SO(4,4)$ and in which electromagnetism and gravitation are unified in a Kaluza-Klein-type theory in six dimensions.
Book Synopsis Group Theory in Physics by : Wu-Ki Tung
Download or read book Group Theory in Physics written by Wu-Ki Tung and published by World Scientific. This book was released on 1985 with total page 372 pages. Available in PDF, EPUB and Kindle. Book excerpt: An introductory text book for graduates and advanced undergraduates on group representation theory. It emphasizes group theory's role as the mathematical framework for describing symmetry properties of classical and quantum mechanical systems.Familiarity with basic group concepts and techniques is invaluable in the education of a modern-day physicist. This book emphasizes general features and methods which demonstrate the power of the group-theoretical approach in exposing the systematics of physical systems with associated symmetry.Particular attention is given to pedagogy. In developing the theory, clarity in presenting the main ideas and consequences is given the same priority as comprehensiveness and strict rigor. To preserve the integrity of the mathematics, enough technical information is included in the appendices to make the book almost self-contained.A set of problems and solutions has been published in a separate booklet.
