A geometrical version of Noether's theorem in supermechanics
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.
scientific article; zbMATH DE number 794408