Physics Department,

Ben Gurion University of the Negev,

84105 Beer Sheva,

ISRAEL

E-mail: daboul@bgu.ac.il, jdaboul@gmail.com

**Saved representations and contraction hysterises of
N-dimensional oscillators plus a constant force**

**Abstract:**

I study the contraction of the $N$-dimensional oscillator with a constant
force ${\bf f}$,

\[

H=\frac {{\bf p}^2}{2m} + \frac k 2 {\bf x}^2- {\bf f} \cdot
{\bf x},

\]

and show that one obtains a `*contraction hysterisis*', as the
parameters $k$ and $f$ approach zero in different order. I show that the
quadrupole moments provide a natural *saved realization* of the contracted
$su(N)$ algebras.

See abstract in PDF.