Spelling suggestions: "subject:"supermanifolds"" "subject:"supermanifold""
1 |
Elementary states, supergeometry and twistor theoryPilato, Alejandro Miguel January 1986 (has links)
It is shown that H<sup>p-1</sup> (P<sup>+</sup>, 0 (-m-p)) is a Fréchet space, and its dual is H<sup>q-1</sup>(P<sup>-</sup>, 0 (m-q)), where P<sup>+</sup> and P<sup>-</sup> are the projectivizations of subsets of generalized twistor space (≌ ℂ<sup>p-q</sup>) on which the hermitian form (of signature (p,q)) is positive and negative definite respectively, and 0(-m-p) denotes the sheaf of germs of holomorphic functions homogeneous of degree -m-p. It is then proven, for p = 2 and q = 2, that the subspace consisting of all twistor elementary states is dense in H<sup>p-1</sup>(P<sup>+</sup>, 0(-m-p)). A supermanifold is a ringed space consisting of an underlying classical manifold and an augmented sheaf of <strong>Z</strong><sub>2</sub>-graded algebras locally isomorphic to an exterior algebra. The subcategory of the category of ringed spaces generated by such supermanifolds is referred to as the super category. A mathematical framework suitable for describing the generalization of Yang-Mills theory to the super category is given. This includes explicit examples of supercoordinate changes, superline bundles, and superconnections. Within this framework, a definition of the full super Yang-Mills equations is given and the simplest case is studied in detail. A comprehensive account of the generalization of twistor theory to the super category is presented, and it is used in an attempt to formulate a complete description of the super Yang-Mills equations. New concepts are introduced, and several ideas which have previously appeared in the literature at the level of formal calculations are expanded and explained within a consistent framework.
|
2 |
It's pretty super! : A Mathematical Study of Superspace in Fourdimensional, Unextended SupersymmetryFriden, Eric January 2012 (has links)
Superspace is a fundamental tool in the study of supersymmetry, one that while often used is seldom defined with a proper amount of mathematical rigor. This paper examines superspace and presents three different constructions of it; the original by Abdus Salam and J. Strathdee as well as two modern methods by Alice Rogers and Buchbinder-Kuzenko.Though the structures arrived at are the same the two modern constructions differ in methods, elucidating different important aspects of super-space. Rogers focuses on the underlying structure through the study of supermanifolds, and Buchbinder-Kuzenko the direct correlation with the Poincare superalgebra, and the parametrisation in terms of exponents.
|
3 |
The Bose/Fermi oscillators in a new supersymmetric representationIhl, Matthias, 1977- 25 October 2011 (has links)
This work deals with the application of supermathematics to supersymmetrical problems arising in physics. Some recent developments are presented in detail. A reduction scheme for general supermanifolds to vector bundles is presented, which significantly simplifies their mathematical treatment in a physical context. Moreover, some applications of this new approach are worked out, such as the Fermi oscillator. / text
|
4 |
Extensions supersymétriques des équations structurelles des supervariétés plongées dans des superespacesBertrand, Sébastien 06 1900 (has links)
No description available.
|
Page generated in 0.0672 seconds