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Lie Groups, Lie Algebras, and Some of Their Applications
This text introduces upper-level undergraduates to Lie group theory and physical applications. It further illustrates Lie group theory's role in several fields of physics. 1974 edition. Includes 75 figures and 17 tables, exercises and problems.
Modern Group Theoretical Methods in Physics
This book contains the proceedings of a meeting that brought together friends and colleagues of Guy Rideau at the Université Denis Diderot (Paris, France) in January 1995. It contains original results as well as review papers covering important domains of mathematical physics, such as modern statistical mechanics, field theory, and quantum groups. The emphasis is on geometrical approaches. Several papers are devoted to the study of symmetry groups, including applications to nonlinear differential equations, and deformation of structures, in particular deformation-quantization and quantum groups. The richness of the field of mathematical physics is demonstrated with topics ranging from pure mathematics to up-to-date applications such as imaging and neuronal models. Audience: Researchers in mathematical physics.
Applications of Group Theory in Physics and Mathematical Physics
The past decade has seen a renewal in the close ties between mathematics and physics. The Chicago Summer Seminar on Applications of Group Theory in Physics and Mathematical Physics, held in July, 1982, was organized to bring together a broad spectrum of scientists from theoretical physics, mathematical physics, and various branches of pure and applied mathematics in order to promote interaction and an exchange of ideas and results in areas of common interest. This volume contains the papers submitted by speakers at the Seminar. The reader will find several groups of articles varying from the most abstract aspects of mathematics to a concrete phenomenological description of some models applicable to particle physics. The papers have been divided into four categories corresponding to the principal topics covered at the Seminar. This is only a rough division, and some papers overlap two or more of these categories.
Progress in String Theory and M-Theory
Recent developments in supersymmetric field theory, string theory, and brane theory have been revolutionary. The main focus of the present volume is developments of M-theory and its applications to superstring theory, quantum gravity, and the theory of elementary particles. Topics included are D-branes, boundary states, and world volume solitons. Anti-De-Sitter quantum field theory is explained, emphasising the way it can enforce the holography principle, together with the relation to black hole physics and the way Branes provide the microscopic interpretation for the entropy of black holes. Developments in D-branes within type-I superstring and related theories are described. There are also possible phenomenological implications of superstring theory that would lie within the range of quantum gravity effects in the future generation of accelerators, around 1 TeV.
Supersymmetry In The Theories Of Fields, Strings & Branes, Procs Of The Advanced School
During the last three decades supersymmetry has grown into one of the busiest theoretical avenues of particle physics. Supersymmetric ideas dominate the scenario of “beyond the standard model phenomenology”, in spite of the thirty-year-old experimental opacity, a situation that could change within the following decade. One additional important reason for the good health of supersymmetry must be found in the most speculative areas of particle physics. Much of its success comes from superstring theory.The Advanced School on Supersymmetry in the Theories of Fields, Strings and Branes attempted to provide an up-to-date perspective of the role played by supersymmetry in these subjects. The le...
Conférence Moshé Flato 1999
These two volumes constitute the Proceedings of the `Conférence Moshé Flato, 1999'. Their spectrum is wide but the various areas covered are, in fact, strongly interwoven by a common denominator, the unique personality and creativity of the scientist in whose honor the Conference was held, and the far-reaching vision that underlies his scientific activity. With these two volumes, the reader will be able to take stock of the present state of the art in a number of subjects at the frontier of current research in mathematics, mathematical physics, and physics. Volume I is prefaced by reminiscences of and tributes to Flato's life and work. It also includes a section on the applications of scie...
Finite Mathematics as the Foundation of Classical Mathematics and Quantum Theory
This book delves into finite mathematics and its application in physics, particularly quantum theory. It is shown that quantum theory based on finite mathematics is more general than standard quantum theory, whilst finite mathematics is itself more general than standard mathematics.As a consequence, the mathematics describing nature at the most fundamental level involves only a finite number of numbers while the notions of limit, infinite/infinitesimal and continuity are needed only in calculations that describe nature approximately. It is also shown that the concepts of particle and antiparticle are likewise approximate notions, valid only in special situations, and that the electric charge and baryon- and lepton quantum numbers can be only approximately conserved.
Superstrings and Related Matters
In this volume, topics such as the AdS/CFT correspondence, non-BPS states, noncommutative gauge theories and the Randall-Sundrum scenario are discussed. For the AdS/CFT correspondence, some of its generalizations, including examples of non-AdS/nonconformal backgrounds, are described. Myer's effect in this context and otherwise is also treated. Recent results in the context of non-BPS states are reviewed, in particular the use of open string field theory in understanding the related problem of tachyon condensation. Instantons and solitons in noncommutative gauge theories are described, as are various issues in the framework of the Randall-Sundrum scenario.
