Departamento de Matematica da Pontificia Universidade Catolica
Rua Marques de Sao Vicente 225
22453 Gavea, Rio de Janeiro, RJ, Brazil
E-mail: svetlich@mat.puc-rio.br

Nonlinear Schroedinger equations for identical particles and the separation property

Abstract:
We investigate the separation property for hierarchies of Schroedinger operators for identical particles.  We show that such hierarchies of translation invariant second order differential operators are necessarily linear. A weakened form of the separation property, related to a strong form of cluster decomposition, allows for homogeneous hierarchies of non linear differential operators. Some connections with the field theoretic formalism in Fock space are pointed out.