Thf3 symposium "Symmetries in Science VIII" was held in August of 1994 at the Cloister Mehrerau in Bregenz, Austria. The symposium was supported by Southern Illinois University at Carbondale, the Land Vorarlberg, and the Landeshaupstaot Bregenz. I wish to thank Dr. John C. Guyon, President of Southern Illinois University at Carbondale; Dr. Hubert Regner, Amt der Vorarlberger Landesregierung; and Dipl. Vw. Siegfried Gasser, Buergermeister der Landeshauptstadt Bregenz and Lantagsabgeordneter, for their generous support of the symposium. Finally I wish to thank Frater Albin of the Cloister Mehrerau for his support and cooperation in this endeavor, which made for a successful meeting in a most pleasant environment. Bruno Gruber v CONTENTS On Om x Gin Highest Weight Vectors Helmer Aslaksen, Eng-Chye Tan, and Chen-bo Zhu ... . Invariant Theory of Matrices Helmer Aslaksen, Eng-Chye Tan, and Chen-bo Zhu ... . 1 3 Symmetries of Elementary Particles Revisited A.O. Barut ... ... ... 21 Perturbative SU(1,1) Haluk Seker ... . ..., . ... 25 A Dual Structure for the Quantal Rotation Group, SU(2) L.C. Biedenharn and M.A. Lohe ..., . ... ... 37 Some Points in the Quantization of Relativistic Grassmann Dependent Interaction Systems A. Del Sol Mesa and R, P. Martinez y Romero ..., . ... 49 for Uq(sl(4)) and q-Conformal q-Difference Intertwining Operators I nvariant Equations V.K. Dobrev ... ... ... 55 A Quantum Mechanical Evolution Equation for Mixed States from Symmetry and Kinematics H.-D. Doebner and J.D. Hennig ... ... 85 vii Quantum Mechanical Motions over the Group Manifolds and Related Potentials I.H. Duru -. ... ... ...

This book is a collection of reviews and essays about the recent developments in the area of Symmetries and applications of Group Theory. Contributions have been written mostly at the graduate level but some are accessible to advanced undergraduates. The book is of interest to a wide audience and covers a broad range of topics with a strong degree of thematical unity. The book is part of a Series of books on Symmetries in Science and may be compared to the published Proceedings of the Colloquia on Group Theoretical Methods in Physics. Here, however, prevails a distinguished character for presenting extended reviews on present applications to Science, not restricted to Theoretical Physics.

Proceedings of a symposium held in Bregenz, Austria, August 6-10, 1996

Proceedings an International Symposium held in Bregenz, Austria, July 13-18, 1997

Southern Illinois University at Carbondale undertook to honor Albert Einstein as scientist and as humanitarian in commemo ration of his lOOth birthday during an "Albert Einstein Centennial Week", February 23 - March 2, 1979. During the course of this week two Symposia were held, entitled "Symmetries in Science" and "Einstein: Humanities Conscience", in addition to cultural and social activities honoring Einstein. This volume presents the Symposium "Symmetries in Science". It reflects the outstanding response that was given to our "Albert Einstein Centennial Week" by the international community of scientists. The motivation to have a celebration honoring Albert Einstein at Southern Illinois University at Carbondale was supplied by Dr. Paul A. Schilpp, the editor of the "Library of Living Philo sophers". Albert Einstein has contributed to this series with his autobiographical notes, a kind of autobiography of his scientific life, in a volume entitled "Einstein: Scientist-Philosopher", the most popular among all the outstanding volumes of this series. Dr. Paul A. Schilpp's presence at Southern Illinois University at Carbondale provided a natural link for an Einstein Celebration as a kind of a continuation of the contribution he made to mankind through the Einstein volume of his "Library of Living Philosophers".

In this book Rickles considers several interpretative difficulties raised by gauge-type symmetries (those that correspond to no change in physical state). The ubiquity of such symmetries in modern physics renders them an urgent topic in philosophy of physics. Rickles focuses on spacetime physics, and in particular classical and quantum general relativity. Here the problems posed are at their most pathological, involving the apparent disappearance of spacetime! Rickles argues that both traditional ontological positions should be replaced by a structuralist account according to which relational structure is what the physics is about. · Unified treatment of gauge symmetries and their relationship to ontology in physics · Brings philosophy of space and time into step with developments in modern physics · Argues against the received view on the implications of symmetries in physics · Provides elementary treatments of technical issues · Illustrates a novel defense of structuralism

Logic, Methodology and Philosophy of Science VIII presents the results of recent research into the foundations of science. The volume contains 37 invited papers presented at the Congress, covering the areas of Logic, Mathematics, Physical Sciences, Biological Sciences and the Humanities.