On a geometric framework for Lagrangian supermechanics

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.

19 pages. Comments welcomed. Minor typos corrected

References in corpus (2)

• Nonholonomic Constraints: a New Viewpoint
• The geodesic flow on a Riemannian supermanifold

Cited by in corpus (2)

• Symplectic ${\mathbb{Z}}_2^n$-manifolds
• The super-Sasaki metric on the antitangent bundle