Semigroup Methods In Supersymmetric Theories Of Elementary Particles
Abstract
Description
The thesis is devoted to abstract, geometric and symmetric aspects of modern elementary particle theories. A new direction in constructing supersymmetric and superstring models based on consequent and strong consideration and inclusion of semigroups, ideals and noninvertible properties into their mathematical structure is proposed. A theory of semisupermanifolds (Chapter I) and noninvertible generalization of superconformal (Chapters II-III) and hyperbolic geometries (Chapter V) are introduced. New continuous supermatrix representations of semigroups (Chapter IV) are obtained. The carried out investigations will allow us to formulate a theoretical model of elementary particles based on supersymmetry in terms of more general categories and new structures - as a theory of abstract and supermatrix semigroups which includes previous theories as a particular invertible case in abstract sense.
Habilitation Thesis in Russian, 483 pp., 3 Figures, 3 Tables, 832 citations, 7 Appendices (for other formats of the thesis, autoreferat (synopsis), and by chapters available from http://gluon.physik.uni-kl.de/~duplij/disser.htm or http://www-home.univer.kharkov.ua/duplij/disserk.htm)
Habilitation Thesis in Russian, 483 pp., 3 Figures, 3 Tables, 832 citations, 7 Appendices (for other formats of the thesis, autoreferat (synopsis), and by chapters available from http://gluon.physik.uni-kl.de/~duplij/disser.htm or http://www-home.univer.kharkov.ua/duplij/disserk.htm)