Multi-particle fermionic realization of the su(2) Lie algebra

M. Yamamura, A. Kuriyama, Teiji Kunihiro

Considering the present situation of Lie-algebraic studies of high-temperature superconductivity, a Schwinger-type boson realization of the su(4) algebra is investigated. The basic framework comes from a possible form of the su(n) and the su(n,1) algebras in the Schwinger representation, which was recently proposed by two of the present authors (M. Y. & A. K.), together with J. da Providência. The form investigated in this paper is, in some sense, a natural extension of the Schwinger boson representation for the so(5), so(4) and su(2)⊗su(2) algebras, which was also proposed by the present authors. The orthogonal set for the irreducible representation of the su(4) algebra is completely analogous to that expressed in terms of fermion operators for pairing correlation.

Mikhail N. Kiselev, Heiko Feldmann, R. Oppermann

L. Frappat, A. Sciarrino, S. Sciuto +1 more

Christopher C. Gerry

A few years ago, Agarwal (1991 Phys. Rev. A 44 8398) showed that the Susskind–Glogower phase operators, expressible in terms of Bose operators, provide a realization of the algebra for particles obeying infinite statistics. In this paper we show that the SU (1, 1) phase operators, constructed in terms of the elements of the su (1, 1) Lie algebra, also provide a realization of the algebra for infinite statistics. There are many realizations of the su (1, 1) algebra in terms of single or multimode bose operators, three of which are discussed along with their corresponding phase states. The Susskind–Glogower phase operator is a special case of the SU (1, 1) phase operator associated with the Holstein–Primakoff realization of su (1, 1).

Fuli Li, Shengli Zhang, Qing Huang

A new multi-fermion realization of is built, whose generators have been written as functions of operators of su(2) algebra. With the help of the realization, the influence of the q-deformation of su(2) algebra on the excitation spectrum and the ground state properties of the Lipkin - Meshkov - Glick model can easily be understood. It is also shown that the variation approach on the basis of the usual su(2) coherent state still works well for the q-deformed model.

L. Frappat, P. Sorba, A. Sciarrino +1 more