Supersymetrie et mathematiques
Francois Gieres
TL;DR
This paper introduces supersymmetry concepts through three examples—supersymmetric quantum mechanics, Lie superalgebras, and Quillen superconnections—highlighting their commonalities and applications in mathematics and physics.
Contribution
It provides an accessible introduction to supersymmetry by illustrating key concepts with concrete examples and discusses their applications and connections to important theorems.
Findings
Outline of the proof of Gauss-Bonnet theorem by Patodi
Explanation of Morse inequalities following Witten
Identification of common features across supersymmetry notions
Abstract
Nous presentons une introduction aux concepts de la supersymetrie par l'intermediaire de trois exemples: (i) Mecanique quantique supersymetrique, (ii) Superalgebres de Lie, (iii) Superconnexions de Quillen. Les points communs a toutes ces notions sont soulignes et des applications sont indiquees. En particulier nous esquissons la demonstration du theoreme de Gauss et Bonnet d'apres Patodi et la demonstration des inegalites de Morse d'apres Witten.
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Taxonomy
TopicsAdvanced Topics in Algebra · Homotopy and Cohomology in Algebraic Topology · Advanced Algebra and Geometry