##### Dr. Stefan Berceanu

I have a program to find a simple geometrical description of coherent states as they are used in Physics:

1) find a geometrical significance for the transition probabilities on manifold of coherent states;

2) find a geometrical description for the phase which appears in the transition amplitude;

3) find all the manifolds for which the angle defined by the scalar product of two normalised coherent states is a distance on the manifold of coherent states;

4) find a geometrical significance for the diastasis function of Calabi in the context of coherent states;

5) state precisely the projective space in which is embedded the manifold of coherent states;

6) state precisely the relationship between the coherent states and geodesics;

7) state precisely the geometrical meaning of the polar divisor (the locus of coherent vectors orthogonal to a fixed coherent vector).

This program has been applied to compact and noncompact hermitian symmetric spaces and now is applied to homogeneous spaces attached to the Jacobi group.

- S. Berceanu, A. Gheorghe,
*On the construction of Perfect Morse functions on compact manifold of coherent states,*J. Math. Phys. 28, 2899-3007 (1987). - S. Berceanu, L. Boutet de Monvel,
*Linear dynamical systems, coherent state manifolds, flows and matrix Riccati,*J. Math. Phys 34, 2353-2371 (1993). - S. Berceanu and M. Schlichenmaier,
*Coherent state embeddings, polar divisors and Cauchy formulas,*J. Geom. Phys. 34, 336-358 (1999). - S. Berceanu,
*A holomorphic representation of the Jacobi algebra,*Rev. Math. Phys., vol. 18, No. 2 163-199 (2006). - S. Berceanu,
*Balanced metric and Berezin quantization on the Siegel-Jacobi ball,*SIGMA 12, 064 (2016).