Boson mappings applied to the two-color delta model

Abstract

We study several aspects of a two-color delta model of interacting quarks, with the purpose of extracting information of relevance to real quark models of nuclei. We first describe a BCS treatment of the quark pair correlations that arise in the model at low densities and demonstrate that the rms radius of the dominant correlated pairs increases in the presence of the medium. We then consider the application of a Dyson boson mapping to the model and show that it incorporates, at the level of the Hartree-Bose approximation, the pair clustering dynamics of quark BCS. However, the collective bosons that emerge do not have the same structure as the correlated BCS pairs. The mapping also leads to a shortrange repulsive interaction between the collective bosons, which we derive in both momentum and coordinate space. The additional correlations that result from this repulsive boson interaction can in principle be incorporated through a Brueckner treatment of the mapped boson Hamiltonian.

Parafermionic mapping of the two-colour delta model of interacting quarks

“…We have shown that in the case of the two-colour delta model of interacting quarks [3,4,5,9,10] there is an exact mapping of quark pairs onto colourless parafermions of order ρ = 2. The situation resembes earlier findings for the single-j nuclear shell, in which nucléon pairs are mapped onto parafermions of order related to the size of the nuclear shell [14].…”

“…Some of the boson mappings of the pairs of fermions are approximate, some others are exact but involve relatively complicated square roots of operators in the relevant formulas, these difficulties being caused by the presence of the Pauli principle. The boson mapping approach has also been applied in the case of the above mentioned quark models with two [9,10] or three [11,12] colours.…”

“…In this paper we attempt to get exact mappings for the two-colour delta model of interacting quarks mentioned above [3,4,5,9,10]. It turns out that an exact mapping of this model can be constructed through the use of parafermions.…”

Mapping of Composite Hadrons into Elementary Hadrons and Effective Hadronic Hamiltonians

“…In order to obtain q (5) and q (5)-, the generator F of the transformation at fourth order is needed.…”

New Mechanism for the Enhancement ofsdDominance in Interacting Boson Models

“…We now return to the set of R operators (6) and search for their mutual eigenvectors. To do this, we follow the procedure introduced by Richardson for the pairing model hamiltonian (7). Namely, we consider the ansatz…”