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Semigroup Methods In Supersymmetric Theories Of Elementary Particles

Steven Duplij
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Abstract

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.

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Steven Duplij. 1999-10-28. Semigroup Methods In Supersymmetric Theories Of Elementary Particles. https://arxiv.org/abs/math-ph/9910045

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