Illustrating the fascinating interplay between physics and mathematics, Groups, Representations and Physics, Second Edition provides a solid foundation in the theory of groups, particularly group representations. For this new, fully revised edition, the author has enhanced the book's usefulness and widened its appeal by adding a chapter on the Cartan-Dynkin treatment of Lie algebras. This treatment, a generalization of the method of raising and lowering operators used for the rotation group, leads to a systematic classification of Lie algebras and enables one to enumerate and construct their irreducible representations. Taking an approach that allows physics students to recognize the power and elegance of the abstract, axiomatic method, the book focuses on chapters that develop the formalism, followed by chapters that deal with the physical applications. It also illustrates formal mathematical definitions and proofs with numerous concrete examples.

Illustrating the fascinating interplay between physics and mathematics, Groups, Representations and Physics, Second Edition provides a solid foundation in the theory of groups, particularly group representations. For this new, fully revised edition, the author has enhanced the book's usefulness and widened its appeal by adding a chapter on the Cartan-Dynkin treatment of Lie algebras. This treatment, a generalization of the method of raising and lowering operators used for the rotation group, leads to a systematic classification of Lie algebras and enables one to enumerate and construct their irreducible representations. Taking an approach that allows physics students to recognize the power and elegance of the abstract, axiomatic method, the book focuses on chapters that develop the formalism, followed by chapters that deal with the physical applications. It also illustrates formal mathematical definitions and proofs with numerous concrete examples.

George Mackey was an extraordinary mathematician of great power and vision. His profound contributions to representation theory, harmonic analysis, ergodic theory, and mathematical physics left a rich legacy for researchers that continues today. This book is based on lectures presented at an AMS special session held in January 2007 in New Orleans dedicated to his memory. The papers, written especially for this volume by internationally-known mathematicians and mathematical physicists, range from expository and historical surveys to original high-level research articles. The influence of Mackey's fundamental ideas is apparent throughout. The introductory article contains recollections from former students, friends, colleagues, and family as well as a biography describing his distinguished career as a mathematician at Harvard, where he held the Landon D. Clay Professorship of Mathematics.

The Mathematical Sciences Research Institute sponsored a three day conference, May 21-23, 1984 to honor Professor George W. Mackey. The title of the conference, Group Representations, Ergodic Theory, Operator Algebras, and Mathematical Physics, reflects the interests in science that have characterized Professor wide ranging Mackey's work. The conference provided an opportunity for his students, friends and colleagues to honor him and his contributions. The conference was attended by over one hundred people and the participants included five mathematical generations Professor Mackey's mathematical father, Marshall Stone, many mathematical children, grandchildren, and at least one mathematical great-grandchild. This volume is a compendium of the scientific papers presented at the conference plus some additional papers contributed after the conference. The far ranging scope of the various articles is a further indication of the large number of fields that have been affected by Professor Mackey's work. Calvin C. Moore Berkeley, CA Feb, 1986 Table of Contents Preface vi i Ambiguity Functions and Group L. Auslander and Representations R. Tolimieri Kirillov Orbits and Direct Integral Lawrence Corwin 11 Decompositions on Certain Quotient Spaces Some Homotopy and Shape Calculations Edward G. Effors and 69 for C*-Algebras Jerome Kaminker 121 Small Unitary Representations of Roger Howe Classical Groups Dual Vector Spaces Irving Kaplansky 151 Exponential Decay of Correlation Calvin C. Moore 163 Coefficients for Geodesic Flows Lattices in U(n. I) G. D. Mostow Induced Bundles and Nonlinear Irving E. Segal 199 Wave equations Compact Ahelian Aut.

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. Request Inspection Copy

The Application of Group Theory in Physics is a 17-chapter text based on a course of lectures concerning the principles, concepts, and application of group theory in physics, given at the Gorki University in Kharkov. This text presents first the parts of the theory of representations of finite and continuous groups that are most important in application. Considerable chapters cover the groups of theory of interest in theoretical physics and demonstrate the principles according to which the abstract concepts and the theorems of representation theory are applied in theoretical physics. The remaining chapters provide representations of the rotation group and the Lorentz group. The closing part of this work contains tables of the detailed description of the 230 space groups and for the characters of certain groups. This book is intended primarily for physicists specializing in theoretical physics

Elements of the theory of groups -- Some specific groups -- The theory of group representations -- Operations with group representations -- Representations of certain groups -- Small oscillations of symmetrical systems -- Second order phase transitions -- Crystals -- Infinite groups -- Representations of the rotation groups in two and three dimensions and of the full orthogonal group -- Clebsch-Gordon and Racah coefficients -- The Schrödinger equation -- Equations invariant under the Euclidean group of motions in space -- Absorption and Raman scattering of light -- Representations of the Lorentz group -- Relativistically invariant equations -- Nuclear reactions.

Recent devopments, particularly in high-energy physics, have projected group theory and symmetry consideration into a central position in theoretical physics. These developments have taken physicists increasingly deeper into the fascinating world of pure mathematics. This work presents important mathematical developments of the last fifteen years in a form that is easy to comprehend and appreciate.