Date/heure
12 décembre 2019
14:30 - 15:30
Oratrice ou orateur
Hovhannes Khuvaderdian
Catégorie d'évènement Séminaire Théorie de Lie, Géométrie et Analyse
Résumé
For an arbitrary morphism of (super)manifolds, the pull-back is a linear map of the space of functions. In 2014 Th.Voronov have introduced thick morphisms of (super)manifolds which define a generally non-linear pull-back of functions. This construction was introduced as an adequate tool to describe L-infinity morphisms of algebras of functions provided with the structure of a homotopy Poisson algebra. It turns out that if you go down from `heaven to earth’, and consider usual (not super!) manifolds, then we come to constructions which have natural interpretation in classical and quantum mechanics. In particular in this case the geometrical object which defines the thick diffeomorphism becomes an action of classsical mecanics, and pull-back of the thick diffeomorphism with a quadratic action give a spinor representation. I will define a thick morphism and will tell shortly about their application in homotopy Poisson algebras. Then I will discuss the relation of thick morphisms with notions such as the action in classical mechanics and spinors. The talk is based on the work: « Thick morphisms of supermanifolds, quantum mechanics and spinor representation’, J.Geom. and Phys., 2019, article Number: 103540, https://doi.org/10.1016/ j.geomphys.2019.103540, arXiv:1909.00290 Authors: Hovhannes Khudaverdian, Theodore Voronov