Group Theory from the Eightfold Way to the Periodic Table
Author: Arnout Ceulemans
Publisher: Oxford University Press
Category: Group theory
The standard model of subatomic particles and the periodic table of the atoms have the common goal to bring order in the bewildering chaos of the constituents of matter. Their success relies on the presence of fundamental symmetries in their core. The purpose of the book is to share theadmiration for the power and the beauty of these symmetries. The reader is taken on a journey from the basic geometric symmetry group of a circle to the sublime dynamic symmetries that govern the motions of the particles. The trail follows the lines of parentage linking groups upstream to theunitary symmetry of the eightfold way of quarks, and to the four-dimensional symmetry of the hydrogen atom. Along the way the theory of symmetry groups is gradually introduced with special emphasis on graphical representations. The final challenge is to open up the structure of Mendeleev's tablewhich goes beyond the symmetry of the hydrogen atom. Breaking this symmetry to accommodate the multi-electron atoms requires to leave the common ground of linear algebras and explore the potential of non-linearity.
The Periodic Table effectively embraces the whole realm of chemistry within the confines of one comparatively simple and easily understood chart of the chemical elements. Over many years the Periodic Table has proven to be indispensable not only to chemists of all kinds but also to a host of other scientists, including biologists, geologists and physicists. It is thus hardly surprising that the Periodic Table has become one of our most celebrated contemporary scientific icons. In the present work various aspects of the Periodic Table that are seldom if ever featured elsewhere are given prominence. The twelve presentations contained herein all have a mathematical flavour because it is the intention to highlight the often-neglected mathematical features of the Periodic Table and several closely related topics. The book starts out by considering predictions of what the ultimate size of the Periodic Table will be when all of the possible artificial chemical elements have been synthesised. It then moves on to an examination of the nature of the periodicity extant in the Periodic Table and some methods for the prediction of the properties of the super-heavy elements. The Periodic Table is next explored in various dimensions other than two. The natural clustering of the elements into groups is studied by three different but complementary routes, namely via the topological structures of the groups, the self-association of the elements as evidenced by neural network studies, and information theoretical analysis of the behaviour of atoms. Following a detailed investigation of the mathematical basis for the periodicity seen in atomic and molecular spectroscopy, three separate presentations delve into many different aspects of the group-theoretical structure of the Periodic Table. The unusual combination of themes offered here will appeal to all who seek a more detailed and intimate knowledge of the Periodic Table than that available in standard texts on the subject.
New edition of a standard introductory text cited in BCL3 . This extended version adds seven completely new chapters on modern physics (an edition sans these chapters is reported available). Annotation copyright Book News, Inc. Portland, Or.
"This series discusses how the major fields of science developed during specific time periods. Each volume focuses on a range of years and includes developments in exploration, life sciences, mathematics, physical sciences, and technology. When the series is completed, the seven volumes will cover 2000 B.C. to the present."--"Outstanding Reference Sources," American Libraries, May 2001.
Publisher: World Scientific Publishing Company Incorporated
This book recalls, for nonscientific readers, the history of quantum mechanics, the main points of its interpretation, and Einstein's objections to it, together with the responses engendered by his arguments. Most popular discussions on the strange aspects of quantum mechanics ignore the fundamental fact that Einstein was correct in his insistence that the theory does not directly describe reality. While that fact does not remove the theory's counterintuitive features, it casts them in a different light. Context is provided by following the history of two central aspects of physics: the elucidation of the basic structure of the world made up of particles, and the explanation, as well as the prediction, of how objects move. This history, prior to quantum mechanics, reveals that whereas theories and discoveries concerning the structure of nature became increasingly realistic, the laws of motion, even as they became more powerful, became more and more abstract and remote from intuitive notions of reality. Newton's laws of motion gained their abstract power by sacrificing direct and intuitive contact with real experience. Arriving 250 years after Newton, the break with a direct description of reality embodied in quantum mechanics was nevertheless profound.