Dynamics determines geometry

Details Dynamics determines geometry Dynamics determines geometry

2012-04-15

arxiv.org/abs/1204.3281v1

Physics

Mathematical Physics

7 pages, no figures

Scientific paper

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.

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