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Theory Of Groups And Symmetries: Representations Of Groups And Lie Algebras, Applications
This book is a sequel to the book by the same authors entitled Theory of Groups and Symmetries: Finite Groups, Lie Groups, and Lie Algebras.The presentation begins with the Dirac notation, which is illustrated by boson and fermion oscillator algebras and also Grassmann algebra. Then detailed account of finite-dimensional representations of groups SL(2, C) and SU(2) and their Lie algebras is presented. The general theory of finite-dimensional irreducible representations of simple Lie algebras based on the construction of highest weight representations is given. The classification of all finite-dimensional irreducible representations of the Lie algebras of the classical series sℓ(n, C), so(n...
Theory Of Groups And Symmetries: Finite Groups, Lie Groups, And Lie Algebras
The book presents the main approaches in study of algebraic structures of symmetries in models of theoretical and mathematical physics, namely groups and Lie algebras and their deformations. It covers the commonly encountered quantum groups (including Yangians). The second main goal of the book is to present a differential geometry of coset spaces that is actively used in investigations of models of quantum field theory, gravity and statistical physics. The third goal is to explain the main ideas about the theory of conformal symmetries, which is the basis of the AdS/CFT correspondence.The theory of groups and symmetries is an important part of theoretical physics. In elementary particle phy...
New Perspectives On Einstein's E = Mc2
Einstein's energy-momentum relation is applicable to particles of all speeds, including the particle at rest and the massless particle moving with the speed of light. If one formula or formalism is applicable to all speeds, we say it is 'Lorentz-covariant.' As for the internal space-time symmetries, there does not appear to be a clear way to approach this problem. For a particle at rest, there are three spin degrees of freedom. For a massless particle, there are helicity and gauge degrees of freedom. The aim of this book is to present one Lorentz-covariant picture of these two different space-time symmetries. Using the same mathematical tool, it is possible to give a Lorentz-covariant picture of Gell-Mann's quark model for the proton at rest and Feynman's parton model for the fast-moving proton. The mathematical formalism for these aspects of the Lorentz covariance is based on two-by-two matrices and harmonic oscillators which serve as two basic scientific languages for many different branches of physics. It is pointed out that the formalism presented in this book is applicable to various aspects of optical sciences of current interest.
Vortex Atom, The: A New Paradigm
With clear illustrations throughout and without recourse to quantum mechanics, the reader is invited to revisit unsolved problems lying at the foundations of theoretical physics. Maxwell and his contemporaries abandoned their search for a geometrical representation of the electric and magnetic fields. The wave-particle dilemma and Bose-Einstein statistical counting have resulted in unsatisfactory non-realistic interpretations. Furthermore, a simple structure of the hydrogen atom that includes hyperfine levels is still wanting.Working with the latest experimental data in photonics a proposed solution to the wave-particle dilemma is suggested based on an array of circular-polarized rays. The Bose-Einstein counting procedure is recast in terms of distinguishable elements. Finally, a vortex model of a 'particle' is developed based on a trapped photon. This consists of a single ray revolving around a toroidal surface, and allows a geometrical definition of mass, electric potential, and magnetic momentum. With the adjustment of two parameters, values to 4 dp for the hyperfine frequencies (MHz) of hydrogen can be obtained for which a computer program is available.
Understanding Gravity: The Generation Model Approach
Currently, the General Theory of Relativity (GTR) describes the physics of the very large in terms of classical physics, while quantum theory describes the physics of the very small in terms of the Standard Model of particle physics. Unfortunately, the two theories are incompatible and do not describe satisfactorily all the forces between the various particles comprising ordinary matter. At present, one of the deepest problems in theoretical physics is harmonizing the GTR, which describes gravitation, with quantum mechanics, which describes the other three fundamental forces acting on the atomic scale. The main aim of the book is to provide an understanding of gravity in terms of a quantum theory given by the Generation Model of particle physics. The book presents a fully quantum theory of gravity, which describes both the large cosmological scale and the small atomic scale interactions between all particles.
Group And Representation Theory
This volume goes beyond the understanding of symmetries and exploits them in the study of the behavior of both classical and quantum physical systems. Thus it is important to study the symmetries described by continuous (Lie) groups of transformations. We then discuss how we get operators that form a Lie algebra. Of particular interest to physics is the representation of the elements of the algebra and the group in terms of matrices and, in particular, the irreducible representations. These representations can be identified with physical observables.This leads to the study of the classical Lie algebras, associated with unitary, unimodular, orthogonal and symplectic transformations. We also d...
Stalingrad
“A fresh look at what is perhaps the most famous battle of the Russo-German War from the Soviet perspective.” —The NYMAS Review Much has been written about the Battle of Stalingrad, the Soviet victory that turned the tide of the Second World War. Yet our knowledge and understanding continues to evolve, and this engrossing account by Alexey Isaev brings together previously unpublished Russian archive material—strategic directives and orders, after-action reports, and official records of all kinds—with the vivid recollections of soldiers who were there, on the front lines, reconstructing what happened in extraordinary new detail. The evidence leads him to question common assumptions ...
String Fields, Higher Spins And Number Theory
The book aims to analyze and explore deep and profound relations between string field theory, higher spin gauge theories and holography — the disciplines that have been on the cutting edge of theoretical high energy physics and other fields. These intriguing relations and connections involve some profound ideas in number theory, which appear to be part of a unifying language to describe these connections.
Russia and the Information Revolution
This work, the result of a six-year study, sheds light on Russia's role in the global Information Revolution. It examines Russia's increasing reliance on information and communications technologies (IT) to improve its government institutions, modernize business and industry and stimulate economic growth, broaden information access, and enhance the quality of life for Russian people. The author examines Russia's emerging IT sector, how businesses in Russia are seeking to use IT to enhance productivity and profitability, the impact of IT on government, and the course of the Information Revolution in Russian society.
