XXVIII Workshop on Geometric Methods in Physics 28.06-04.07.2009

Stefan Berceanu

S. Berceanu, The Jacobi group and the squeezed states - some comments.

After recalling the main properties of the Jacobi group $G^J_1$ and its relationship with he squeezed states of quantum optics, we show effectively the orthonormality of the base functions with respect with the scalar product. Imposing hermitian conjugacy to the generators of the Jacobi algebra, we find out the form of the weight function appearing in the scalar product. From the explicit form of the reproducing kernel, we find out the expression multiplier in the representation of the Jacobi group $G^J_1$.