Dynamics determines geometry

Abstract

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.

7 pages, no figures

References in corpus (4)

• Magnetic fields in noncommutative quantum mechanics
• Magnetic-Dipole Spin Effects in Noncommutative Quantum Mechanics
• Aharonov-Bohm effect in a Class of Noncommutative Theories
• Spin Non-commutativity and the Three-Dimensional Harmonic Oscillator