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Hamiltonian versus Lagrangian formulations of supermechanics

Hamiltonian versus Lagrangian formulations of supermechanics 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of Physics A: Mathematical and General IOP Publishing

Hamiltonian versus Lagrangian formulations of supermechanics

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Copyright
Copyright © IOP Publishing Ltd
ISSN
0305-4470
eISSN
1361-6447
DOI
10.1088/0305-4470/30/8/017
Publisher site
See Article on Publisher Site

Abstract

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.

Journal

Journal of Physics A: Mathematical and GeneralIOP Publishing

Published: Apr 21, 1997

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