Reference : On a geometric framework for Lagrangian supermechanics
Scientific journals : Article
Physical, chemical, mathematical & earth Sciences : Mathematics
On a geometric framework for Lagrangian supermechanics
Bruce, Andrew mailto [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit >]
Grabowska, Katarzyna mailto [University of Warsaw, Poland > Faculty of Physics]
Moreno, Giovanni mailto [Polish Academy of Sciences > Institute of Mathematics]
The Journal of Geometric Mechanics
American Institute of Mathematics
411 - 437
[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

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