Dr. Stefan Berceanu
Senior Researcher I
University of Bucharest, 1976
+40-(0)21-4046247 (ext. 3403)
206
theoretical physics, mathematical physics and mathematics geometrical methods in quantum mechanics
geometrical methods in quantum mechanics, differential geometry, group theoretical methods in physics, coherent states

 

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.

 

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