English

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.

Keywords

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

R2 v1 2026-06-22T14:20:40.542Z