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| Author | : Fergus Rae O'Dea |
| Publisher | : |
| Total Pages | : 154 |
| Release | : 2000 |
| Genre | : Harmonic maps |
| ISBN | : |
| Author | : John C. Wood |
| Publisher | : Springer-Verlag |
| Total Pages | : 328 |
| Release | : 2013-07-02 |
| Genre | : Mathematics |
| ISBN | : 366314092X |
| Author | : Idrisse Khemar |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 234 |
| Release | : 2012 |
| Genre | : Mathematics |
| ISBN | : 0821869256 |
In this paper, the author studies all the elliptic integrable systems, in the sense of C, that is to say, the family of all the $m$-th elliptic integrable systems associated to a $k^\prime$-symmetric space $N=G/G_0$. The author describes the geometry behind this family of integrable systems for which we know how to construct (at least locally) all the solutions. The introduction gives an overview of all the main results, as well as some related subjects and works, and some additional motivations.
| Author | : Christopher Kum Anand |
| Publisher | : CRC Press |
| Total Pages | : 332 |
| Release | : 1999-10-13 |
| Genre | : Mathematics |
| ISBN | : 9781584880325 |
The subject of harmonic morphisms is relatively new but has attracted a huge worldwide following. Mathematicians, young researchers and distinguished experts came from all corners of the globe to the City of Brest - site of the first, international conference devoted to the fledgling but dynamic field of harmonic morphisms. Harmonic Morphisms, Harmonic Maps, and Related Topics reports the proceedings of that conference, forms the first work primarily devoted to harmonic morphisms, bringing together contributions from the founders of the subject, leading specialists, and experts in other related fields. Starting with "The Beginnings of Harmonic Morphisms," which provides the essential background, the first section includes papers on the stability of harmonic morphisms, global properties, harmonic polynomial morphisms, Bochner technique, f-structures, symplectic harmonic morphisms, and discrete harmonic morphisms. The second section addresses the wider domain of harmonic maps and contains some of the most recent results on harmonic maps and surfaces. The final section highlights the rapidly developing subject of constant mean curvature surfaces. Harmonic Morphisms, Harmonic Maps, and Related Topics offers a coherent, balanced account of this fast-growing subject that furnishes a vital reference for anyone working in the field.
| Author | : V. S. Varadarajan |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 311 |
| Release | : 2004 |
| Genre | : Mathematics |
| ISBN | : 0821835742 |
An special feature of the book is the treatment in depth of the theory of spinors in all dimensions and signatures, which is the basis of all developments of supergeometry both in physics and mathematics, especially in quantum field theory and supergravity."--Jacket.
| Author | : Richard H. Cushman |
| Publisher | : Birkhäuser |
| Total Pages | : 449 |
| Release | : 2012-12-06 |
| Genre | : Science |
| ISBN | : 3034888910 |
This book gives a complete global geometric description of the motion of the two di mensional hannonic oscillator, the Kepler problem, the Euler top, the spherical pendulum and the Lagrange top. These classical integrable Hamiltonian systems one sees treated in almost every physics book on classical mechanics. So why is this book necessary? The answer is that the standard treatments are not complete. For instance in physics books one cannot see the monodromy in the spherical pendulum from its explicit solution in terms of elliptic functions nor can one read off from the explicit solution the fact that a tennis racket makes a near half twist when it is tossed so as to spin nearly about its intermediate axis. Modem mathematics books on mechanics do not use the symplectic geometric tools they develop to treat the qualitative features of these problems either. One reason for this is that their basic tool for removing symmetries of Hamiltonian systems, called regular reduction, is not general enough to handle removal of the symmetries which occur in the spherical pendulum or in the Lagrange top. For these symmetries one needs singular reduction. Another reason is that the obstructions to making local action angle coordinates global such as monodromy were not known when these works were written.
| Author | : Mauro Carfora |
| Publisher | : World Scientific |
| Total Pages | : 194 |
| Release | : 1992-04-30 |
| Genre | : |
| ISBN | : 9814554766 |
This volume contains lectures on recent advances in the theory of integrable systems and quantum groups. It introduces the reader to attractive areas of current research.
| Author | : Henrik Aratyn |
| Publisher | : Springer |
| Total Pages | : 400 |
| Release | : 1998-01-28 |
| Genre | : Mathematics |
| ISBN | : |
This book combines supersymmetry modelling in quantum mechanics and integrable models in a unique way. It addresses researchers as well as graduate students. Along with articles that present new technical results, the reader will also find pedagogically written reviews. Recent applications of supersymmetric integrable models are also given.
| Author | : C. Fronsdal |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 280 |
| Release | : 2012-12-06 |
| Genre | : Science |
| ISBN | : 9400946244 |
to our own also needs to be understood. Such unification may also require that the supersymmetry group possess irreducible representations with infinite reductiori on the Poincare subgroup, to accommodate an infinite set of particles. Such possibilities were 5 envisaged long ago and have recently reappeared in Kaluza-Klein . 6 d' . th 7 S . l' th supergraVlty an m superstnng eory. upersymmetry Imp Ies at forces that are mediated by bose exchange must be complemented by forces that are due to the exchange of fermions. The masslessness of neutrinos is suggestive-we continue to favor the idea that neutrinos are fundamental to weak interactions, that they will finally play a more central role than the bit part assigned to them in Weinberg-Salam theory. There seems to be little room for doubting that supersymmetry is badly broken-so where should one be looking for the first tangible manifestations of it? It is remarkable that the successes that can be legitimately claimed for supersymmetry are all in the domain of massless particles and fields. Supergravity is not renormalizable, but it is an improvement (in this respect) over ordinary quantum gravity. Finite super Yang-Mills theories are not yet established, but there is now a strong concensus that they soon will be. In both cases massless fields are involved in an essential way.
| Author | : Claudio Carmeli |
| Publisher | : European Mathematical Society |
| Total Pages | : 308 |
| Release | : 2011 |
| Genre | : Lie algebras |
| ISBN | : 9783037190975 |
Supersymmetry is a highly active area of considerable interest among physicists and mathematicians. It is not only fascinating in its own right, but there is also indication that it plays a fundamental role in the physics of elementary particles and gravitation. The purpose of the book is to lay down the foundations of the subject, providing the reader with a comprehensive introduction to the language and techniques, as well as detailed proofs and many clarifying examples. This book is aimed ideally at second-year graduate students. After the first three introductory chapters, the text is divided into two parts: the theory of smooth supermanifolds and Lie supergroups, including the Frobenius theorem, and the theory of algebraic superschemes and supergroups. There are three appendices. The first introduces Lie superalgebras and representations of classical Lie superalgebras, the second collects some relevant facts on categories, sheafification of functors and commutative algebra, and the third explains the notion of Frechet space in the super context.
