%0 Journal Article
%T Dynamics determines geometry
%A Sergio A. Hojman
%A J. Gamboa
%A F. Mendez
%J Physics
%D 2012
%I arXiv
%R 10.1142/S0217732312501866
%X The inverse problem of calculus of variations and $s$-equivalence are re-examined by using results obtained from non-commutative geometry ideas. The role played by the structure of the modified Poisson brackets is discussed in a general context and it is argued that classical $s$-equivalent systems may be non-equivalent at the quantum mechanical level. This last fact is explicitly discussed comparing different approaches to deal with the Nair-Polychronakos oscillator.
%U http://arxiv.org/abs/1204.3281v1