Abstract
The choice of a coordinate chart on an analytical Rn(Rna) provides a representation of the n-dimensional supersymmetric oscillator. The 1-parameter group of dilations provides a Euclidean evolution moving the system through a sequence of charts, that at each instant supply a Hilbert space by Cartan’s exterior algebra endowed with a suitable scalar product. Stationary states and coherent states are eigenstates of the Lie derivatives generating the dilations and the translations, respectively.
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