Nilpotent Classical Mechanics

The formalism of nilpotent mechanics is introduced in the Lagrangian and Hamiltonian form. Systems are described using nilpotent, commuting coordinates \(\eta\). Necessary geometrical notions and elements of generalized differential \(\eta\)-calculus are introduced. The so called \(s-\)geometry, in...

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Bibliographic Details
Published in:arXiv.org 2007-03
Main Author: Frydryszak, Andrzej M
Format: Article
Language:English
Subjects:
Calculus
Classical mechanics
Differential calculus
Differential geometry
Mechanics (physics)
Supersymmetry
Symmetry
Online Access:Get full text
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Summary:The formalism of nilpotent mechanics is introduced in the Lagrangian and Hamiltonian form. Systems are described using nilpotent, commuting coordinates \(\eta\). Necessary geometrical notions and elements of generalized differential \(\eta\)-calculus are introduced. The so called \(s-\)geometry, in a special case when it is orthogonally related to a traceless symmetric form, shows some resemblances to the symplectic geometry. As an example of an \(\eta\)-system the nilpotent oscillator is introduced and its supersymmetrization considered. It is shown that the \(R\)-symmetry known for the Graded Superfield Oscillator (GSO) is present also here for the supersymmetric \(\eta\)-system. The generalized Poisson bracket for \((\eta,p)\)-variables satisfies modified Leibniz rule and has nontrivial Jacobiator.
ISSN:2331-8422
DOI:10.48550/arxiv.0609072