Group Theoretical Methods in Physics: Proceedings of the Fifth International Colloquium provides information pertinent to the fundamental aspects of group theoretical methods in physics. This book provides a variety of topics, including nuclear collective motion, complex Riemannian geometry, quantum mechanics, and relativistic symmetry. Organized into six parts encompassing 64 chapters, this book begins with an overview of the theories of nuclear quadrupole dynamics. This text then examines the conventional approach in the determination of superstructures. Other chapters consider the Hamiltonian formalism and how it is applied to the KdV equation and to a slight variant of the KdV equation. This book discusses as well the significant differential equations of mathematical physics that are integrable Hamiltonian systems, including the equations governing self-induced transparency and the motion of particles under an inverse square potential. The final chapter deals with the decomposition of the tensor product of two irreducible representations of the symmetric group into a direct sum of irreducible representations. This book is a valuable resource for physicists.

Thirty years ago Albert Einstein died, his dream of a theory that would unify the universe unfulfilled. He spent the last decades of his life searching for such a theory-a theory that would explain everything from elementary particles and their interac tions to the overall structure of the universe. But he failed, not because he didn't try hard enough, but because the attempt was ahead of its time. When Einstein worked on the problem liter ally nothing was known about black holes, white holes, sin gularities, the Big Bang explosion and the early universe, quarks, gauge invariance, and weak and strong nuclear forces. Today we know that all these things are important in relation to a unified theory, and that they must be incorporated in and explained by such a theory. Thus, in a sense, our problem is much more complex today than it was in Einstein's day. But scientists have persevered and as a result we are now tan talizingly close to achieving this long-sought goal. Important breakthroughs have been made. In this book we will look at these breakthroughs and at recent unified theories-theories that go by the names supergravity, superstrings, GUTs, and twistor theory. In order to understand the problem, however, we must begin at the beginning.

First published in1966, here is presented a comprehensive overview of one of the most elusive scientific speculations by the pre-eminent genius of the 20th century. The theory is viewed by some scientists with deep suspicion, by others with optimism, but all agree that it represents an extreme challenge. As the author herself affirms, this work is not intended to be a complete treatise or ‘didactic exposition’ of the theory of unified fields, but rather a tool for further study, both by students and professional physicists. Dealing with all the major areas of research which together comprise the development of a working model, the author ranges over conservation equations, variational principles, solutions of spherical symmetry, and treats a wide selection of Einstein’s own equations. The final chapter indicates problems associated with the unified field theory, in particular the energy-momentum tensor and geodesics.

The Mechanical Theory of Everything is a comprehensive and unifying look at how the universe works. Through fresh insights and rigorous derivations, readers will learn: where energy comes from, how a photon dissipates in ten billion years, what electrons and protons are made of, the solution to Einstein s Unified Field theory, how language is made, and why we age. The evidence presented is compelling and spectacular that the universe in which we live is mechanical.

Why did Einstein tirelessly study unified field theory for more than thirty years? In this book, the author argues that Einstein believed he could find a unified theory of all of nature's forces by repeating the methods he thought he had used when he formulated general relativity. The book discusses Einstein's route to the general theory of relativity, focusing on the philosophical lessons that he learnt. It then addresses his quest for a unified theory for electromagnetism and gravity, discussing in detail his efforts with Kaluza-Klein and, surprisingly, the theory of spinors. From these perspectives, Einstein's critical stance towards the quantum theory comes to stand in a new light. This book will be of interest to physicists, historians and philosophers of science.

Advances made by physicists in understanding matter, space, and time and by astronomers in understanding the universe as a whole have closely intertwined the question being asked about the universe at its two extremesâ€"the very large and the very small. This report identifies 11 key questions that have a good chance to be answered in the next decade. It urges that a new research strategy be created that brings to bear the techniques of both astronomy and sub-atomic physics in a cross-disciplinary way to address these questions. The report presents seven recommendations to facilitate the necessary research and development coordination. These recommendations identify key priorities for future scientific projects critical for realizing these scientific opportunities.

This advanced textbook provides an up-to-date and comprehensive introduction to the very active field of structure formation in cosmology. It is written by eleven world-leading authorities. Written in a clear and pedagogical style appropriate for graduate students in astronomy and physics, this textbook introduces the reader to a wide range of exciting topics in contemporary cosmology: from recent advances in redshift surveys, to the latest models in gravitational lensing and cosmological simulations. The authors are all world-renowned experts both for their research and teaching skills. In the fast-moving field of structure formation, this book provides advanced undergraduate and graduate students with a welcome textbook which unites the latest theory and observations.