Lagrangian and Noncommutativity

Details Lagrangian and Noncommutativity Lagrangian and Noncommutativity

2003-05-07

arxiv.org/abs/hep-th/0305045v2

Physics

High Energy Physics

High Energy Physics - Theory

25 pag. Latex. Reference added

Scientific paper

We analyze the relation between the concept of auxiliary variables and the Inverse problem of the calculus of variations to construct a Lagrangian from a given set of equations of motion. The problem of the construction of a consistent second order dynamics from a given first order dynamics is investigated. At the level of equations of motion we find that this reduction process is consistent provided that the mapping of the boundary data be taken properly into account. At the level of the variational principle we analyze the obstructions to construct a second order Lagrangian from a first order one and give an explicit formal non-local Lagrangian that reproduce the second order projected dynamics. Finally we apply our ideas to the so called ``Noncommutative classical dynamics''.

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