A geometrical version of Noether's theorem in supermechanics
type: Item
instance of: scholarly article
title: A geometrical version of Noether's theorem in supermechanics
zbMATH Open document ID: 0846.58008
DOI: 10.1016/0034-4877(94)90002-7
author: Héctor Figueroa
author: J. F. Cariñena
published in: Reports on Mathematical Physics
publication date: 1996-09-26T00:00:00Z
full work available at URL: http://cds.cern.ch/record/272063
review text: The authors generalize the concepts of vector fields and forms along maps to graded geometry and apply them to the study of Lagrangian supermechanics, in particular to the converse of Noether's theorem. They review the concepts of supermanifold, morphism, tangent supermanifold etc. Then prolongations of supervector fields along the tangent projection are studied. An analogue of the concept of second-order differential equation and the concept of semibasic form are considered to prepare a generalized version of Noether's theorem in supermechanics. Thus finally the authors have establishes a one-to-one correspondence between the generalized symmetries and first integrals of the dynamics defined by a superlagrangian.
Mathematics Subject Classification ID: 58C50
Mathematics Subject Classification ID: 70H33
Mathematics Subject Classification ID: 58A50
zbMATH DE Number: 794408
zbMATH Keywords: graded geometry
zbMATH Keywords: Lagrangian supermechanics
zbMATH Keywords: Noether's theorem
zbMATH Keywords: supervector fields
reviewed by: Grigori L. Litvinov
MaRDI profile type: Publication
OpenAlex ID: W2092657202
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description: scientific article; zbMATH DE number 794408