On a geometric framework for Lagrangian supermechanics
Mathematical Physics
2018-04-26 v2 High Energy Physics - Theory
Differential Geometry
math.MP
Quantum Algebra
Abstract
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.
Cite
@article{arxiv.1606.02604,
title = {On a geometric framework for Lagrangian supermechanics},
author = {Andrew James Bruce and Katarzyna Grabowska and Giovanni Moreno},
journal= {arXiv preprint arXiv:1606.02604},
year = {2018}
}
Comments
19 pages. Comments welcomed. Minor typos corrected