The concept of symmetric space is of central importance in many branches of mathematics. Compactifications of these spaces have been studied from the points of view of representation theory, geometry, and random walks. This work is devoted to the study of the interrelationships among these various compactifications and, in particular, focuses on the martin compactifications. It is the first exposition to treat compactifications of symmetric spaces systematically and to uniformized the various points of view.

Key features:

* definition and detailed analysis of the Martin compactifications

* new geometric Compactification, defined in terms of the Tits building, that coincides with the Martin Compactification at the bottom of the positive spectrum.

* geometric, non-inductive, description of the Karpelevic Compactification

* study of the well-know isomorphism between the Satake compactifications and the Furstenberg compactifications

* systematic and clear progression of topics from geometry to analysis, and finally to random walks

The work is largely self-contained, with comprehensive references to the literature. It is an excellent resource for both researchers and graduate students.

The concept of symmetric space is of central importance in many branches of mathematics. Compactifications of these spaces have been studied from the points of view of representation theory, geometry, and random walks. This work is devoted to the study of the interrelationships among these various compactifications and, in particular, focuses on the martin compactifications. It is the first exposition to treat compactifications of symmetric spaces systematically and to uniformized the various points of view. The work is largely self-contained, with comprehensive references to the literature. It is an excellent resource for both researchers and graduate students.

One of the paradoxes of the physical sciences is that as our knowledge has progressed, more and more diverse physical phenomena can be explained in terms of fewer underlying laws, or principles. In Hidden Unity, eminent physicist John Taylor puts many of these findings into historical perspective and documents how progress is made when unexpected, hidden unities are uncovered between apparently unrelated physical phenomena. Taylor cites examples from the ancient Greeks to the present day, such as the unity of celestial and terrestrial dynamics (17th century), the unity of heat within the rest of dynamics (18th century), the unity of electricity, magnetism, and light (19th century), the unity of space and time and the unification of nuclear forces with electromagnetism (20th century). Without relying on mathematical detail, Taylor's emphasis is on fundamental physics, like particle physics and cosmology. Balancing what is understood with the unestablished theories and still unanswered questions, Taylor takes readers on a fascinating ongoing journey. John C. Taylor is Professor Emeritus of Mathematical Physics at the University of Cambridge. A student of Nobel laureate Abdus Salam, Taylor's research career has spanned the era of developments in elementary particle physics since the 1950s. He taught theoretical physics at Imperial College, London, and at the Universities of Oxford and Cambridge, and he has lectured worldwide. He is a Fellow of the Royal Society and a Fellow of the Institute of Physics.

Paul Adrian Maurice Dirac, one of the greatest physicists of the twentieth century, died in 1984. Dirac's college, St John's of Cambridge, generously endowed annual lectures to be held at Cambridge University in his memory. This 1990 volume includes an expanded version of the third Dirac Memorial Lecture presented by Abdus Salam, in addition to two previously unpublished lectures by Paul Dirac and by Werner Heisenberg.

This is an expanded version of the third Dirac Memorial Lecture, given in 1988 by the Nobel Laureate Abdus Salam. Salam's lecture presents an overview of the developments in modern particle physics from its inception at the turn of the century to the present theories seeking to unify all the fundamental forces. In addition, two previously unpublished lectures by Paul Dirac, and Werner Heisenberg are included. These lectures provide a fascinating insight into their approach to research and the developments in particle physics at that time. Nonspecialists, undergraduates and researchers will find this a fascinating book. It contains a clear introduction to the major themes of particle physics and cosmology by one of the most distinguished contemporary physicists.

One of the paradoxes of the physical sciences is that as our knowledge has progressed, more and more diverse physical phenomena can be explained in terms of fewer underlying laws, or principles. In Hidden Unity, eminent physicist John Taylor puts many of these findings into historical perspective and documents how progress is made when unexpected, hidden unities are uncovered between apparently unrelated physical phenomena. Taylor cites examples from the ancient Greeks to the present day, such as the unity of celestial and terrestrial dynamics (17th century), the unity of heat within the rest of dynamics (18th century), the unity of electricity, magnetism, and light (19th century), the unity of space and time and the unification of nuclear forces with electromagnetism (20th century). Without relying on mathematical detail, Taylor's emphasis is on fundamental physics, like particle physics and cosmology. Balancing what is understood with the unestablished theories and still unanswered questions, Taylor takes readers on a fascinating ongoing journey. John C. Taylor is Professor Emeritus of Mathematical Physics at the University of Cambridge. A student of Nobel laureate Abdus Salam, Taylor's research career has spanned the era of developments in elementary particle physics since the 1950s. He taught theoretical physics at Imperial College, London, and at the Universities of Oxford and Cambridge, and he has lectured worldwide. He is a Fellow of the Royal Society and a Fellow of the Institute of Physics.

This scarce antiquarian book is a selection from Kessinger Publishing's Legacy Reprint Series. Due to its age, it may contain imperfections such as marks, notations, marginalia and flawed pages. Because we believe this work is culturally important, we have made it available as part of our commitment to protecting, preserving, and promoting the world's literature. Kessinger Publishing is the place to find hundreds of thousands of rare and hard-to-find books with something of interest for everyone!

This scarce antiquarian book is a selection from Kessinger Publishing's Legacy Reprint Series. Due to its age, it may contain imperfections such as marks, notations, marginalia and flawed pages. Because we believe this work is culturally important, we have made it available as part of our commitment to protecting, preserving, and promoting the world's literature. Kessinger Publishing is the place to find hundreds of thousands of rare and hard-to-find books with something of interest for everyone!

This scarce antiquarian book is a selection from Kessinger Publishing's Legacy Reprint Series. Due to its age, it may contain imperfections such as marks, notations, marginalia and flawed pages. Because we believe this work is culturally important, we have made it available as part of our commitment to protecting, preserving, and promoting the world's literature. Kessinger Publishing is the place to find hundreds of thousands of rare and hard-to-find books with something of interest for everyone!