Supermanifolds And Supergroups
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| Author | : Gijs M. Tuynman |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 424 |
| Release | : 2006-01-20 |
| Genre | : Mathematics |
| ISBN | : 1402022972 |
Supermanifolds and Supergroups explains the basic ingredients of super manifolds and super Lie groups. It starts with super linear algebra and follows with a treatment of super smooth functions and the basic definition of a super manifold. When discussing the tangent bundle, integration of vector fields is treated as well as the machinery of differential forms. For super Lie groups the standard results are shown, including the construction of a super Lie group for any super Lie algebra. The last chapter is entirely devoted to super connections. The book requires standard undergraduate knowledge on super differential geometry and super Lie groups.
| Author | : C. Bartocci |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 255 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 9401135045 |
'Et moi ... - si favait III mmment en revenir, One service mathematics has rendered the je n'y serais point aile:' human race. It has put CXlUImon sense back Iules Verne where it belongs. on the topmost shelf next to the dUlty canister lahelled 'discarded non- The series i. divergent; therefore we may be able to do something with it. Eric T. Bell O. Hesvi.ide Mathematics is a tool for thOUght. A highly necessary tool in a world where both feedback and non linearities abound. Similarly, all kinds of parts of mathematics serve as tools for other parts and for other sciences. Applying a simple rewriting rule to the quote on the right above one finds such statements as: 'One service topology has rendered mathematical physics .. .'; 'One service logic has rendered com puter science .. .'; 'One service category theory has rendered mathematics .. .'. All arguably true. And all statements obtainable this way form part of the raison d't!tre of this series.
| Author | : T. Voronov |
| Publisher | : CRC Press |
| Total Pages | : 152 |
| Release | : 1991 |
| Genre | : Mathematics |
| ISBN | : 9783718651993 |
The author presents the first detailed and original account of his theory of forms on supermanifolds-a correct and non-trivial analogue of Cartan-de Rham theory based on new concepts. The paper develops the apparatus of supermanifold differential topology necessary for the integration theory. A key feature is the identification of a class of proper morphisms intimately connected with Berezin integration, which are of fundamental importance in various problems. The work also contains a condensed introduction to superanalysis and supermanifolds, free from algebraic formalism, which sets out afresh such challenging problems as the Berezin intgegral on a bounded domain.
| Author | : Rita Fioresi |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 77 |
| Release | : 2012 |
| Genre | : Mathematics |
| ISBN | : 0821853007 |
In the framework of algebraic supergeometry, the authors give a construction of the scheme-theoretic supergeometric analogue of split reductive algebraic group-schemes, namely affine algebraic supergroups associated to simple Lie superalgebras of classical type. In particular, all Lie superalgebras of both basic and strange types are considered. This provides a unified approach to most of the algebraic supergroups considered so far in the literature, and an effective method to construct new ones. The authors' method follows the pattern of a suitable scheme-theoretic revisitation of Chevalley's construction of semisimple algebraic groups, adapted to the reductive case. As an intermediate step, they prove an existence theorem for Chevalley bases of simple classical Lie superalgebras and a PBW-like theorem for their associated Kostant superalgebras.
| Author | : S. Duplij |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 472 |
| Release | : 2012-12-06 |
| Genre | : Science |
| ISBN | : 9401008361 |
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.
| Author | : C. Bartocci |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 274 |
| Release | : 1991-10-31 |
| Genre | : Mathematics |
| ISBN | : 9780792314400 |
'Et moi, ...* si favait III mmment en revenir, One service mathematics has rendered the je n'y serais point aile:' human race. It has put CXlUImon sense back Iules Verne where it belongs. on the topmost shelf next to the dUlty canister lahelled 'discarded non- The series i. divergent; therefore we may be able to do something with it. Eric T. Bell O. Hesvi.ide Mathematics is a tool for thOUght. A highly necessary tool in a world where both feedback and non linearities abound. Similarly, all kinds of parts of mathematics serve as tools for other parts and for other sciences. Applying a simple rewriting rule to the quote on the right above one finds such statements as: 'One service topology has rendered mathematical physics .. .'; 'One service logic has rendered com puter science .. .'; 'One service category theory has rendered mathematics .. .'. All arguably true. And all statements obtainable this way form part of the raison d't!tre of this series.
| Author | : Leonardo Castellani |
| Publisher | : World Scientific Publishing Company |
| Total Pages | : 2220 |
| Release | : 1991-06-11 |
| Genre | : |
| ISBN | : 9814590738 |
This book provides a self-contained presentation of supergravity theories from its fundamentals to its most recent union with string and superstring theories, which are also reviewed in a self-contained manner. The subject is presented consistently in a unified geometric formalism, relying on the calculus of exterior forms and the mathematics needed to develop the theory is explained in appropriate chapters.
| Author | : S. Sternberg |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 312 |
| Release | : 2001-11-30 |
| Genre | : Science |
| ISBN | : 9781402003417 |
The following pages represent the Proceedings of the XI Annual Conference on Differential Geometric Methods in Mathematical Physics which was held in Jerusalem from August 5 through 11, 1982 under the auspices of the Tel Aviv University and the Israel Academy of Sciences and Humanities. In addition to the above mentioned institutions, partial financial support was received form the Bank Leumi Lelsrael Fund for International Conferences, the American Friends of the Tel Aviv Institute of Mathematical Sciences and the Mathematics and Physics Branch of the United States Army Research, Development and Standardization Group (UK). We are grateful to all of these organizations for their financial support. GAUGE THEORY AND NUCLEAR STRUCTURE K. Bleuler Institut fur Theoretische Kernphysik der Universitat Bonn NuBallee 14-16, D-5300 Bonn, West-Germany I. INTRODUCTION The recent, most impressive verification of the Salam -Weinberg theory of electro-weak interactions through the experimental discovery of the so-called inter mediate bosons represents, at the same time, a success of the general gauge theoretical viewpoints in modern particle physics (quantum chromodynamics, 0CD). This theory leads to a deeper and by far more natural inter pretation of particle interaction and induces, as we shall see, also a profound change in our understanding of nuclear structure.
| Author | : Bryce Dewitt |
| Publisher | : CUP Archive |
| Total Pages | : 340 |
| Release | : 1984 |
| Genre | : Science |
| ISBN | : 9780521311762 |
This book presents a detailed exposition of the modern theory of supermanifolds, including a rigorous account of the super-analogs of all the basic structures of ordinary manifold theory. The exposition opens with the theory of analysis over supernumbers (Grassmann variables), Berezin integration, supervector spaces and the superdeterminant. This basic material is then applied to the theory of supermanifolds, with an account of the super-analog of Lie derivatives, connections, metrics, curvature, geodesics, Killing flows, conformal groups, etc. The book goes on to discuss the theory of super Lie groups, super Lie algebras, and invariant geometrical structures on coset spaces. Complete descriptions are given of all the simple super Lie groups. The final chapter contains an account of the Peierls bracket for superclassical dynamical systems, super Hilbert spaces, path integration for fermionic quantum systems, and simple models of Bose-Fermi supersymmetry. Many exercises are included to supplement the material in the text.
| Author | : Carina Boyallian |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 169 |
| Release | : 2011 |
| Genre | : Mathematics |
| ISBN | : 0821852590 |
Focuses on representation theory, harmonic analysis in Lie groups, and mathematical physics related to Lie theory. The papers give a broad overview of these subjects and also of the recent developments in research.
