Orthosymplectic Supersymmetry and its Application to Nuclear Physics.
Abstract
Phenomenological models have long been employed by nuclear physicists to explain systematic trends in data. The Geometrical Model of Bohr, Mottelson and Rainwater (GM) and the Interacting Boson Model (IBM) are two such models that have been used to study the spectra of eveneven nuclei. The IBM differs from previous boson models in that the total number of bosons is conserved and finite. In the GM the bosons of lowest angular momentum have l = 2 and are taken to represent quadrupole shape vibrations, whereas in the IBM the bosons are generally taken to have l = 0, 2 and can be interpreted as correlated pairs of fermions. These models have been extended to handle the neighboring oddeven nuclei by considering the interaction of a fermion with the bosonic space. If the fermionic space consists of the singleparticle angular momenta j _1, j_2, ..., then the largest group describing this mixed system of bosons and fermions is the product group U^{rm B}(5) times U^{rm F}(m_{rm j} ) (GM) or U^{rm B} (6) times U^ {rm F}(m_{rm j}) (IBM), where m_{rm j} = Sigma(2j _{rm i} + 1). If one of the subgroups of U^{rm B} (5) or U^{rm B}(6) is isomorphic to one of the subgroups of U^ {rm F}(m_{rm j}), then we can combine the two group chains into a common bosefermi group chain. These combined bose fermi groups have been used extensively in the Interacting BosonFermion Model (IBFM) to study oddeven nuclei and have been claimed as evidence for the existence of supersymmetries; however, the superalgebras associated with these supersymmetries were never identified. We have identified, for the first time, the superalgebras that are associated with some of these combined bosefermi symmetries. This superalgebra, the noncompact orthosymplectic superalgebra Osp(4s+2/2,R), is fundamentally different than those previously used in the IBFM, where the product algebra was simply embedded into the superalgebra U(6/m _{rm j}). The U(6/m _{rm j}) superalgebras do not imply any particular coupling scheme, and hence cannot be associated with any particular one of the combined bosefermi algebras. The last few chapters are devoted to a study of coherent states for the noncompact orthosymplectic supergroups Osp(1/2N,R) and Osp(2/2N,R), although the results generalize rather easily to the compact versions of these supergroups. These coherent states, besides being of mathematical interest, form the basis for a study of Osp(M/2N,R) coherent states. (Abstract shortened with permission of author.).
 Publication:

Ph.D. Thesis
 Pub Date:
 1988
 Bibcode:
 1988PhDT.......193S
 Keywords:

 Physics: Nuclear; Mathematics