Quantum groups are a generalization of the classical Lie groups and Lie algebras and provide a natural extension of the concept of symmetry fundamental to physics. This monograph is a survey of the major developments in quantum groups, using an original approach based on the fundamental concept of a tensor operator. Using this concept, properties of both the algebra and co-algebra are developed from a single uniform point of view, which is especially helpful for understanding the noncommuting co-ordinates of the quantum plane, which we interpret as elementary tensor operators. Representations of the q-deformed angular momentum group are discussed, including the case where q is a root of unity, and general results are obtained for all unitary quantum groups using the method of algebraic induction. Tensor operators are defined and discussed with examples, and a systematic treatment of the important (3j) series of operators is developed in detail. This book is a good reference for graduate students in physics and mathematics.
Quantum groups are a generalization of the classical Lie groups and Lie algebras and provide a natural extension of the concept of symmetry fundamental to physics. This monograph is a survey of the major developments in quantum groups, using an original approach based on the fundamental concept of a tensor operator. Using this concept, properties of both the algebra and co-algebra are developed from a single uniform point of view, which is especially helpful for understanding the noncommuting co-ordinates of the quantum plane, which we interpret as elementary tensor operators. Representations of the q-deformed angular momentum group are discussed, including the case where q is a root of unity, and general results are obtained for all unitary quantum groups using the method of algebraic induction. Tensor operators are defined and discussed with examples, and a systematic treatment of the important (3j) series of operators is developed in detail. This book is a good reference for graduate students in physics and mathematics.
This book describes a relativistic quantum theory developed by the author starting from the E.C.G. Stueckelberg approach proposed in the early 40s. In this framework a universal invariant evolution parameter (corresponding to the time originally postulated by Newton) is introduced to describe dynamical evolution. This theory is able to provide solutions for some of the fundamental problems encountered in early attempts to construct a relativistic quantum theory. A relativistically covariant construction is given for which particle spins and angular momenta can be combined through the usual rotation group Clebsch-Gordan coefficients. Solutions are defined for both the classical and quantum two body bound state and scattering problems. The recently developed quantum Lax-Phillips theory of semi group evolution of resonant states is described. The experiment of Lindner and coworkers on interference in time is discussed showing how the property of coherence in time provides a simple understanding of the results. The full gauge invariance of the Stueckelberg-Schroedinger equation results in a 5D generalization of the usual gauge theories. A description of this structure and some of its consequences for both Abelian and non-Abelian fields are discussed. A review of the basic foundations of relativistic classical and quantum statistical mechanics is also given. The Bekenstein-Sanders construction for imbedding Milgrom's theory of modified spacetime structure into general relativity as an alternative to dark matter is also studied.
In 1941, E.C.G. Stueckelberg wrote a paper, based on ideas of V. Fock, that established the foundations of a theory that could covariantly describe the classical and quantum relativistic mechanics of a single particle. Horwitz and Piron extended the applicability of this theory in 1973 (to be called the SHP theory) to the many-body problem. It is the purpose of this book to explain this development and provide examples of its applications. We first review the basic ideas of the SHP theory, both classical and quantum, and develop the appropriate form of electromagnetism on this dynamics. After studying the two body problem classically and quantum mechanically, we formulate the N-body problem. We then develop the general quantum scattering theory for the N-body problem and prove a quantum mechanical relativistically covariant form of the Gell-Mann-Low theorem. The quantum theory of relativistic spin is then developed, including spin-statistics, providing the necessary apparatus for Clebsch-Gordan additivity, and we then discuss the phenomenon of entanglement at unequal times. In the second part, we develop relativistic statistical mechanics, including a mechanism for stability of the off-shell mass, and a high temperature phase transition to the mass shell. Finally, some applications are given, such as the explanation of the Lindneret alexperiment, the proposed experiment of Palacios et al which should demonstrate relativistic entanglement (at unequal times), the space-time lattice, low energy nuclear reactions and applications to black hole physics.
The mechanics of Newton and Galileo is based on the postulate of a universal time which plays the role of an evolution parameter as well as establishing dynamical correlations between interacting systems. The Michelson-Morley experiment, explained by Einstein in terms of Lorentz transformations, appeared to imply that the time is not absolute, but rather suffers from changes when a system is in motion. Einstein's thought experiment involving a moving system and a laboratory frame of observation, however, indicates that the action of the Lorentz transformation corresponds to an observed effect recorded in the laboratory on a clock that must be running in precise synchronization with that of the observed system. Therefore one concludes that there must be a universal time, as postulated by Newton, and the time that suffers Lorentz transformation becomes an observable dynamical variable. This book describes the effect this observation had on the development of the theory of Stueckelberg, Horwitz and Piron, and the corresponding conceptual basis for many phenomena which can be described in a relativistically covariant framework.
Unique in its structure, Federal Income Taxation presents core materials that cover the basics of tax law and also offers “cells” at the end of each chapter that are self-contained units with more in-depth discussion of certain topics. This flexible structure allows professors to customize their tax course by selecting only the additional in-depth materials they want to use. The stellar author team, with years of scholarship and teaching experience, presents a core text that covers the leading cases and explains the substantive tax law that is essential to a basic understanding of federal income tax law and principles. The self-contained, optional units at the end of the book — “cells” —supplement the core text by providing additional material and treat a limited number of topics in greater detail. Notes and questions provide background information and place the cases and statutes in context. More than 150 problems are interspersed throughout the core text and the cells that challenge students to apply the Code, regulations, and income tax theory to specific situations. A detailed Teacher’s Manual provides comments and suggestions for teaching both the core and the cell material as well as answers to all of the questions and problems in the casebook. New to the 6th Edition: Legislative developments, including tax provisions contained in the 2020 Coronavirus Aid, Relief, and Economic Security Act, the 2021 American Rescue Plan Act, and the 2022 Inflation Reduction Act. New cases reflecting developments since the previous edition All materials updated to reflect regulatory and other developments since the previous edition interpreting, responding to, or otherwise relating to, the 2017 Tax Cuts and Jobs Act changes. Professors and students will benefit from: New cases reflecting developments since the previous edition. Core text (about 500 pages) that covers the leading cases and explains the substantive tax law that is essential to a basic understanding of federal income tax law and principles. Novel "Cells," self-contained, optional units at the end of each chapter that supplement the core text by presenting additional material and treating a limited number of topics in greater detail. Notes and questions providing background information and placing the cases and statutes in context. More than 150 problems throughout the core text and cells that challenge students to apply theory to specific situations. An annual "inflation supplement" that provides updated problems and answers to reflect inflation adjustments for the upcoming year, as well as updated tables where relevant.
This book presents classical relativistic mechanics and electrodynamics in the Feynman-Stueckelberg event-oriented framework formalized by Horwitz and Piron. The full apparatus of classical analytical mechanics is generalized to relativistic form by replacing Galilean covariance with manifest Lorentz covariance and introducing a coordinate-independent parameter τ to play the role of Newton's universal and monotonically advancing time. Fundamental physics is described by the τ-evolution of a system point through an unconstrained 8D phase space, with mass a dynamical quantity conserved under particular interactions. Classical gauge invariance leads to an electrodynamics derived from five τ-dependent potentials described by 5D pre-Maxwell field equations. Events trace out worldlines as τ advances monotonically, inducing pre-Maxwell fields by their motions, and moving under the influence of these fields. The dynamics are governed canonically by a scalar Hamiltonian that generates evolution of a 4D block universe defined at τ to an infinitesimally close 4D block universe defined at τ+dτ. This electrodynamics, and its extension to curved space and non-Abelian gauge symmetry, is well-posed and integrable, providing a clear resolution to grandfather paradoxes. Examples include classical Coulomb scattering, electrostatics, plane waves, radiation from a simple antenna, classical pair production, classical CPT, and dynamical solutions in weak field gravitation. This classical framework will be of interest to workers in quantum theory and general relativity, as well as those interested in the classical foundations of gauge theory.
Backed with over 20 years of writing, teaching and professional experience with electronic spreadsheets, the authors have perfected the format and presentation of material for every type learning style. Comprehensive information for students at many levels of experience and a flexible binding make this a must-have series for applications essentials. Areas covered include taking a tour of Excel, creating a worksheet, improving worksheet appearance, producing/printing well-designed worksheet, working with functions, sorting and filtering lists, working with charts, developing a multiple-sheet workbook, creating special effects in a worksheet, changing data in a workbook, formatting and displaying worksheets, documenting/protecting worksheets, integrating applications, using functions to create/analyze data, creating pivot tables and pivot charts and hyperlinks and collaborative tools, designing online forms with Excel, automating tasks with macros, using database functions, expanding charting skills, auditing and customizing worksheets, guiding cell entry--data validation, using problem-solving tools and managing data from multiple sources. For training professionals.
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