Status  Confirmed 
Seminar Series  MATHIHES 
Subjects  hepth 
Date  Thursday 5 December 2019 
Time  14:30 
Institute  IHES 
Seminar Room  Amphithéâtre Léon Motchane 
Speaker's Last Name  Khudaverdian 
Speaker's First Name  Hovhannes 
Speaker's Email Address  
Speaker's Institution  University of Manchester & IHES 
Title  Thick morphisms of supermanifolds, quantum mechanics and spinor representation 
Abstract  For an arbitrary morphism of (super)manifolds, the pullback is a linear map of the space of functions. In 2014 Th.Voronov have introduced thick morphisms of (super)manifolds which define a generally nonlinear pullback of functions. This construction was suggested as an adequate tool to describe 𝐿∞ 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 mechanics, and pullback 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 
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