Antisymmetry in Strangeness -1 and -2 Three-Baryon Systems

Abstract

Using the generalized Pauli principle by adding particle labels to the usual space and spin labels a symmetric Hamiltonian and a corresponding antisymmetric wavefunction is constructed for systems of three baryons in the strangeness sectors $S=-1$ and -2. Applications are the $\Xi NN-\Lambda\Lambda N$ and $NN\Lambda -NN\Sigma$ systems. Minimal sets of generalized coupled Faddeev equations for breakup and rearrangement operators as well as (possible) bound states are derived which have the ordinary Pauli principle among identical particles built in. The equations found confirm our previous sets of coupled Faddeev equations for those systems whose derivation was carried through for distinguishable particles and not using the generalized Pauli principle.