The braided algebra and its Jordan-Schwinger construction in terms of Q-deformed fermionic oscillators

Abstract

The standard bosonic and fermionic Jordan-Schwinger constructions for the Lie algebra of SU(2) are reviewed in this thesis. It is shown that the Jordan-Schwinger constructions of the quantum group with q as deformation parameter SUq(2) are obtained by using q-deformed bosonic and fermionic oscillators. The construction of the braided algebra BMq(2) of Hermitian braided matrices in terms of two independent q-bosonic oscillators in the Fock space is studied. It is also determined that the braided algebra of BMq(2) can be constructed by a pair of q, q -1 deformed bosonic oscillators. By means of a similar approach we construct the braided algebra of (nonHermitian) BMq(2) braided matrices in terms of two independent q-deformed fermionic oscillators. We also observe that the representations of this algebra of q, q -1 deformed fermionic oscillators are constructed in a complex vector space. Finally, in the limit q - 1, we show that our construction gives the Pauli exclusion principle.