Boson-fermion and baryon mapping: Construction of collective subspaces.
1. Theory

Jutta Meyer

jmeyer.i.theory.pdf (PrePrint)

Date: 19911010

Article: published in J. Math. Phys. 33 (10), October 1992

PACS96: 03.65.Fd Algebraic methods
PACS96: 12.40.-y Other models for strong interactions
PACS96: 21.60.-n Nuclear-structure models and methods

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.

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