Modified Pauli matrix and spin algebra from the Z(2)-decomposition of the parafermionic Fock space

Abstract

In this paper the Z(2)-decomposition of the bosonic Fock space and the projection operators for each subspace are considered. Using these, we obtain two kinds of step operators obeying trilinear relation which resembles the parafermion algebra. The Z(2)-decomposition of the parafermionic Fock space is also investigated and a new kind of finite-dimensional algebra obeying the trilinear relation which resembles the parafermion algebra of order p. Finally, the modified Pauli matrices and the modified spin algebra are introduced from the Z(2)-decomposition of the parafermionic Fock space.