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SUMMARY:Thick Morphisms of Supermanifolds\, Quantum Mechanics and Spinor R
epresentation
DTSTART;VALUE=DATE-TIME:20191205T133000Z
DTEND;VALUE=DATE-TIME:20191205T143000Z
DTSTAMP;VALUE=DATE-TIME:20210511T132345Z
UID:indico-event-5414@indico.math.cnrs.fr
DESCRIPTION:For an arbitrary morphism of (super)manifolds\, the pull-back
is a linear map of the space of functions. In 2014 Th.Voronov have introdu
ced thick morphisms of (super)manifolds which define a generally non-linea
r pull-back of functions. This construction was suggested as an adequate t
ool to describe $L_\\infty$ morphisms of algebras of functions provided wi
th the structure of a homotopy Poisson algebra. It turns out that if you g
o down from `heaven to earth'\, and consider usual (not super!) manifolds\
, then we come to constructions which have natural interpretation in class
ical and quantum mechanics. In particular in this case the geometrical obj
ect which defines the thick diffeomorphism becomes an action of classsical
mechanics\, and pull-back of the thick diffeomorphism with a quadratic ac
tion 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 act
ion in classical mechanics and spinors.\n\nThe talk is based on the work:
"Thick morphisms of supermanifolds\, quantum mechanics and spinor represen
tation'\, J.Geom. and Phys.\, 2019\, article Number: 103540\,\nhttps://doi
.org/10.1016/j.geomphys.2019.103540\,\narXiv:1909.00290\nAuthors: Hovhanne
s Khudaverdian\, Theodore Voronov \n\nhttps://indico.math.cnrs.fr/event/54
14/
LOCATION:I.H.E.S. Amphithéâtre Léon Motchane
URL:https://indico.math.cnrs.fr/event/5414/
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