Hamiltonian versus Lagrangian formulations of supermechanic

Details Hamiltonian versus Lagrangian formulations of supermechanic Hamiltonian versus Lagrangian formulations of supermechanic

1997-03-24

arxiv.org/abs/dg-ga/9703016v1

J.Phys.A30:2705-2724,1997

Physics

Mathematical Physics

Plain TeX, 24 pages. Submitted to J. Phys. A

Scientific paper

10.1088/0305-4470/30/8/017

We take advantage of different generalizations of the tangent manifold to the context of graded manifolds, together with the notion of super section along a morphism of graded manifolds, to obtain intrinsic definitions of the main objects in supermechanics such as, the vertical endomorphism, the canonical and the Cartan's graded forms, the total time derivative operator and the super--Legendre transformation. In this way, we obtain a correspondence between the Lagrangian and the Hamiltonian formulations of supermechanics.

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