**Author:****Jutta Meyer****Files:****jmeyer.i.theory.pdf (PrePrint)**

**Date:**19911010**Article:**published in J. Math. Phys. 33 (10), October 1992**Classification:****PACS96**: 03.65.Fd Algebraic methods**PACS96**: 12.40.-y Other models for strong interactions**PACS96**: 21.60.-n Nuclear-structure models and methods**Abstract:**Recently, the mathematical formalism of the Dyson boson mapping has been extended to a system of 3n fermions, leading to the boson-fermion and the baryon mapping. In the present paper, the case of restriction to a subset of three-fermion quantum numbers, the collective indices, is discussed. A theory is developed for the representation of fermionic states and operators in a truncated ideal space where only collective boson-fermion pairs or collective ideal baryons are allowed. An exact reproduction of physical properties is proved to be possible provided that the original fermionic problem can be solved in a subspace where all three-fermion subsystems carry collective indices. Examples of simple applications are presented in the subsequent papers of this series.

Metadata by Thomas Severiens on 3 December 1998

Supporting work done by Sandra Valeska Bergmann.