There are many approaches to noncommutative geometry and its use in physics, the ? operator algebra and C -algebra one, the deformation quantization one, the qu- tum group one, and the matrix algebra/fuzzy geometry one. This volume introduces and develops the subject by presenting in particular the ideas and methods recently pursued by Julius Wess and his group. These methods combine the deformation quantization approach based on the - tion of star product and the deformed (quantum) symmetries methods based on the theory of quantum groups. The merging of these two techniques has proven very fruitful in order to formulate ?eld theories on noncommutative spaces. The aim of the book is to give an introduction to these topics and to prepare the reader to enter the research ?eld himself/herself. This has developed from the constant interest of Prof. W. Beiglboeck, editor of LNP, in this project, and from the authors experience in conferences and schools on the subject, especially from their interaction with students and young researchers. In fact quite a few chapters in the book were written with a double purpose, on the one hand as contributions for school or conference proceedings and on the other handaschaptersforthepresentbook.Thesearenowharmonizedandcomplemented by a couple of contributions that have been written to provide a wider background, to widen the scope, and to underline the power of our methods.

A presentation of outstanding achievements and ideas, of both eastern and western scientists, both mathematicians and physicists. Their presentations of recent work on quantum field theory, supergravity, M-theory, black holes and quantum gravity, together with research into noncommutative geometry, Hopf algebras, representation theory, categories and quantum groups, take the reader to the forefront of the latest developments. Other topics covered include supergravity and branes, supersymmetric quantum mechanics and superparticles, (super) black holes, superalgebra representations, and SUSY GUT phenomenology. Essential reading for workers in the modern methods of theoretical and mathematical physics.

This book contains the extended lectures of the 8th Adriatic meeting which is traditionally devoted to the presentation of lectures on the most advanced scientific topics to young scientists, who actively participate, on an international level, in the development of their respective fields. The emphasis of the present meeting was on gauge theories, particle phenomenology, string theories and cosmology. The accompanying CD-ROM contains 27 additional contributions, of a length somewhat shorter than 25 presented in the printed book.  

The Adriatic Meetings have traditionally been conferences on the most - vanced status of science. They are one of the very few conferences in physics aiming at a very broad participation of young and experienced researchers with di?erent backgrounds in particle physics. Particle physics has grown into a highly multi-faceted discipline over the sixty years of its existence, mainly because of two reasons: Particle physics as an experimental science is in need of large-scale laboratory set-ups, involving typically collaborations of several hundreds or even thousands of researchers and technicians with the most diverse expertise. This forces particle physics, being one of the most fundamental dis- plines of physics, to maintain a constant interchange and contact with other disciplines, notably solid-state physics and laser physics, cosmology and - trophysics, mathematical physics and mathematics. Since the expertise necessary in doing research in particle physics has become tremendously demanding in the last years, the ?eld tends to organize purely expert conferences, meetings and summer schools, such as for detector development, for astroparticle physics or for string theory. TheAdriaticMeetingthroughitsentirehistoryhasbeenaplaceforest- lishing exchange between theory and experiment. The 9th Adriatic Meeting successfully continued this tradition and even intensi?ed the cross-discipline communication by establishing new contacts between the community of c- mologists and of particle physicists. The exchange between theorists and - perimentalists was impressively intensive and will certainly have a lasting e?ect on several research projects of the European and world-wide physics community.

Quantum mechanics, formulated by Werner Heisenberg in 1925, belongs among the greatest achievements of physics. "Fundamental Physics: Heisenberg and Beyond" combines personal tributes to Werner Heisenberg with assessments of his impact on current and future developments in physics. The first part presents two essays commemorating Werner Heisenberg's 100th birthday, and these are complemented by a short and nicely illustrated biographical note in the appendix. In the second part, incisive articles by ten world-leading scientists explain important developments in fundamental physics to a broader community of interested scientists.

The Adriatic Meetings have traditionally been conferences on the most - vanced status of science. They are one of the very few conferences in physics aiming at a very broad participation of young and experienced researchers with di?erent backgrounds in particle physics. Particle physics has grown into a highly multi-faceted discipline over the sixty years of its existence, mainly because of two reasons: Particle physics as an experimental science is in need of large-scale laboratory set-ups, involving typically collaborations of several hundreds or even thousands of researchers and technicians with the most diverse expertise. This forces particle physics, being one of the most fundamental dis- plines of physics, to maintain a constant interchange and contact with other disciplines, notably solid-state physics and laser physics, cosmology and - trophysics, mathematical physics and mathematics. Since the expertise necessary in doing research in particle physics has become tremendously demanding in the last years, the ?eld tends to organize purely expert conferences, meetings and summer schools, such as for detector development, for astroparticle physics or for string theory. TheAdriaticMeetingthroughitsentirehistoryhasbeenaplaceforest- lishing exchange between theory and experiment. The 9th Adriatic Meeting successfully continued this tradition and even intensi?ed the cross-discipline communication by establishing new contacts between the community of c- mologists and of particle physicists. The exchange between theorists and - perimentalists was impressively intensive and will certainly have a lasting e?ect on several research projects of the European and world-wide physics community.

This volume contains important contributions to various topics of modern theoretical physics: supermembranes, supersymmetry, and quantum field theory and quantum groups. The book is dedicated to the late D. Volkov and also contains a selection of his pioneering work in spin and statistics, supersymmetry, supergravity, and superstrings.

This book is a collection of papers in honour of Victor I. Ogievetsky. It contains reviews on supersymmetry and supergravity, dualities, integrable systems, W (super)algebras and quantum symmetries. The reader will also find reprints of some of Ogievetsky's pioneering work on supersymmetry.

The traditional purpose of the Adriatic Meeting is to present most advanced scienti?c research conducted by the lecturers who take part in the development of their ?elds and, in addition, to provide a school-like atmosphere for young scientists. Dubrovnik, as a geographical centre of this region of Europe, provided a most adequate location for this conference. Having very agreeable surroundings, the conference site nevertheless gave a focus for very strong scienti?c interaction. The subjects chosen for the 8th meeting, in September 2001, were gauge theories, particle phenomenology, string theories and cosmology. We were able to bring together a very good cross section of outstanding scientists who gave extraorinarily good presentations. Certainely one reason for this success is that most of us feel obliged to help the scienti?c life in South East Europe return to its former level. However, there are very exciting new scienti?c developments as well. Part of the meeting was dominated by neutrino physics which has just seen exciting progress by establishing neutrino masses experimentally. This was d- cussed within neutrino masses and grand uni?ed theories (GUTs). General - pects of neutrino physics and CP violation, neutrino mixing and the bayron asymmetry were presented along the same lines. On the theoretical side the idea of the construction of gauge theories on non-commutative spaces and their phenomenological implications is accepted worldwide within the particle physics community.

Although the Standard Model of strong and electroweak interactions describesparticle physics phenomena up to the vector boson mass scale very well, it is in general believed that it is not the ultimate theory. The aim of this series of seminars was to initiate discussions between field theorists and phenomenologically oriented high energy physicists on the observable consequenses of the concept of SUSY. The subjects covered by the individual contributions include an introduction to the basic features of SUSY models, in particular the minimal supersymmetric Standard Model, followed by discussions of the theoretical predictions and experimental findings on the particle content and mass spectra, cosmological consequenses, indirect manifestations through quantum effects, radiative corrections in the supersymmetric Higgs sector, and the concept of dynamical electroweak symmetry breaking in the context ofSUSY. These topics are treated at a level appropriate for advanced students.However, the book should also be useful for teachers and researchers.

Quantum mechanics, formulated by Werner Heisenberg in 1925, belongs among the greatest achievements of physics. "Fundamental Physics: Heisenberg and Beyond" combines personal tributes to Werner Heisenberg with assessments of his impact on current and future developments in physics. The first part presents two essays commemorating Werner Heisenberg's 100th birthday, and these are complemented by a short and nicely illustrated biographical note in the appendix. In the second part, incisive articles by ten world-leading scientists explain important developments in fundamental physics to a broader community of interested scientists.

There are many approaches to noncommutative geometry and its use in physics, the ? operator algebra and C -algebra one, the deformation quantization one, the qu- tum group one, and the matrix algebra/fuzzy geometry one. This volume introduces and develops the subject by presenting in particular the ideas and methods recently pursued by Julius Wess and his group. These methods combine the deformation quantization approach based on the - tion of star product and the deformed (quantum) symmetries methods based on the theory of quantum groups. The merging of these two techniques has proven very fruitful in order to formulate ?eld theories on noncommutative spaces. The aim of the book is to give an introduction to these topics and to prepare the reader to enter the research ?eld himself/herself. This has developed from the constant interest of Prof. W. Beiglboeck, editor of LNP, in this project, and from the authors experience in conferences and schools on the subject, especially from their interaction with students and young researchers. In fact quite a few chapters in the book were written with a double purpose, on the one hand as contributions for school or conference proceedings and on the other handaschaptersforthepresentbook.Thesearenowharmonizedandcomplemented by a couple of contributions that have been written to provide a wider background, to widen the scope, and to underline the power of our methods.

A presentation of outstanding achievements and ideas, of both eastern and western scientists, both mathematicians and physicists. Their presentations of recent work on quantum field theory, supergravity, M-theory, black holes and quantum gravity, together with research into noncommutative geometry, Hopf algebras, representation theory, categories and quantum groups, take the reader to the forefront of the latest developments. Other topics covered include supergravity and branes, supersymmetric quantum mechanics and superparticles, (super) black holes, superalgebra representations, and SUSY GUT phenomenology. Essential reading for workers in the modern methods of theoretical and mathematical physics.

Dieses Buch legt der Mechanik weitgehend algebraische Vorstellungen und Methoden, wie sie in der Quantenmechanik bis hin zur Feldtheorie entwickelt wurden, zu Grunde. Die Mechanik dient somit auch der Einfuhrung solcher Methoden, die dann in anderen Bereichen der theoretischen Physik erforderlich werden. Neue Methoden mussen dann nicht mehr bei der Behandlung nicht bekannter physikalischer Vorstellungen neu erarbeitet werden. Schon die Struktur des Raumes, wie auch die Newtonschen Gesetze werden so eingefuhrt, dass sie ein Verstandnis fur moderne, weitergehende Vorstellungen zulassen. Symmetrien und Erhaltungssatze werden von Anfang an betont und es wird gezeigt, wie Erhaltungssatze zu weitreichenden Vorhersagen fur spezifische Systeme fuhren. Die Methode der Loesung von Differentialgleichungen durch Greensche Funktionen, wie sie heute in der Feldtheorie ublich ist, wird schon an Hand der harmonischen Schwingungen eingefuhrt. Feldtheoretische Vorstellungen, wie die Behandlung der schwingenden Saite, werden aus mechanischen Konzepten entwickelt und die relativistische Mechanik wird gleich im Zusammenhang mit elektromagnetischen Vorgangen gesehen. Die kanonische Mechanik bereitet den UEbergang zu quantisierten Systemen vor.

This widely acclaimed introduction to N = 1 supersymmetry and supergravity is aimed at readers familiar with relativistic quantum field theory who wish to learn about the supersymmetry algebra. In this new volume Supersymmetry and Supergravity has been greatly expanded to include a detailed derivation of the most general coupling of super-symmetric gauge theory to supergravity. The final result is the starting point for phenomenological studies of supersymmetric theories. The book is distinguished by its pedagogical approach to supersymmetry. It develops several topics in advanced field theory as the need arises. It emphasizes the logical coherence of the subject and should appeal to physicists whose interests range from the mathematical to the phenomenological. In praise of the first edition: "A beautiful exposition of the original ideas of Wess and Zumino in formulating N = 1 supersymmetry and supergravity theories, couched in the language of superfields introduced by Strathdee and the reviewer.... All] serious students of particle physics would do well to acquire a copy."--Abdus Salam, Nature "An excellent introduction to this exciting area of theoretical physics."--C. J. Isham, Physics Bulletin