[en] supermechanics ; supermanifolds ; Lagrangian systems

[en] We re--examine classical mechanics with both commuting and anticommuting degrees of freedom. We do this by defining the phase dynamics of a general Lagrangian system as an implicit differential equation in the spirit of Tulczyjew. Rather than parametrising our basic degrees of freedom by a specified Grassmann algebra, we use arbitrary supermanifolds by following the categorical approach to supermanifolds.

Polish National Science Centre grant DEC-2012/06/A/ST1/00256

H2020 ; 654721 - GEOGRAL - Geometry of Grassmannian Lagrangian manifolds and their submanifolds, with applications to nonlinear partial differential equations of physical interest