Complex Differential Geometry and Supermanifolds in Strings and Fields

Complex Differential Geometry and Supermanifolds in Strings and Fields
Author: Petrus J.M. Bongaarts
Publisher: Springer
Total Pages: 268
Release: 1988-10-12
Genre: Mathematics
ISBN:

This volume deals with one of the most active fields of research in mathematical physics: the use of geometric and topological methods in field theory. The emphasis in these proceedings is on complex differential geometry, in particular on Kähler manifolds, supermanifolds, and graded manifolds. From the point of view of physics the main topics were field theory, string theory and problems from elementary particle theory involving supersymmetry. The lectures show a remarkable unity of approach and are considerably related to each other. They should be of great value to researchers and graduate students.

Complex Differential Geometry and Supermanifolds in Strings and Fields

Complex Differential Geometry and Supermanifolds in Strings and Fields
Author: Petrus J.M. Bongaarts
Publisher: Springer
Total Pages: 254
Release: 2014-03-12
Genre: Science
ISBN: 9783662136966

This volume deals with one of the most active fields of research in mathematical physics: the use of geometric and topological methods in field theory. The emphasis in these proceedings is on complex differential geometry, in particular on Kähler manifolds, supermanifolds, and graded manifolds. From the point of view of physics the main topics were field theory, string theory and problems from elementary particle theory involving supersymmetry. The lectures show a remarkable unity of approach and are considerably related to each other. They should be of great value to researchers and graduate students.

Supermanifolds

Supermanifolds
Author: Alice Rogers
Publisher: World Scientific
Total Pages: 262
Release: 2007
Genre: Mathematics
ISBN: 9812708855

This book aims to fill the gap in the available literature on supermanifolds, describing the different approaches to supermanifolds together with various applications to physics, including some which rely on the more mathematical aspects of supermanifold theory. The first part of the book contains a full introduction to the theory of supermanifolds, comparing and contrasting the different approaches that exist. Topics covered include tensors on supermanifolds, super fibre bundles, super Lie groups and integration theory. Later chapters emphasise applications, including the superspace approach to supersymmetric theories, super Riemann surfaces and the spinning string, path integration on supermanifolds and BRST quantization.

Quantum Fields and Strings: A Course for Mathematicians

Quantum Fields and Strings: A Course for Mathematicians
Author: Pierre Deligne
Publisher: American Mathematical Society
Total Pages: 747
Release: 2000-04-27
Genre: Mathematics
ISBN: 0821820125

A run-away bestseller from the moment it hit the market in late 1999. This impressive, thick softcover offers mathematicians and mathematical physicists the opportunity to learn about the beautiful and difficult subjects of quantum field theory and string theory. Cover features an intriguing cartoon that will bring a smile to its intended audience.

Noncommutative Structures in Mathematics and Physics

Noncommutative Structures in Mathematics and Physics
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.

String Theory Research Progress

String Theory Research Progress
Author: Ferenc N. Balogh
Publisher: Nova Publishers
Total Pages: 246
Release: 2008
Genre: Business & Economics
ISBN: 9781604560756

String theory is a model of fundamental physics whose building blocks are one-dimensional extended objects called strings, rather than the zero-dimensional point particles that form the basis for the standard model of particle physics. The phrase is often used as shorthand for Superstring theory, as well as related theories such as M-theory. By replacing the point-like particles with strings, an apparently consistent quantum theory of gravity emerges. Moreover, it may be possible to 'unify' the known natural forces (gravitational, electromagnetic, weak nuclear and strong nuclear) by describing them with the same set of equations. Studies of string theory have revealed that it predicts higher-dimensional objects called branes. String theory strongly suggests the existence of ten or eleven (in M-theory) space-time dimensions, as opposed to the usual four (three spatial and one temporal) used in relativity theory.

The Geometry of Supermanifolds

The Geometry of Supermanifolds
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.