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Communications in Theoretical Physics

Bose Description of Pauli Spin Operators and Related Coherent States

Nian-Quan Jiang, Fan Hong‐Yi, Lu Hai-Liang

Published Jan 1, 2005• 0 citations
Publisher

Abstract

Using both the fermionic-like and the bosonic-like properties of the Pauli spin operators σ + , σ − , and σ z we discuss the derivation of Bose description of the Pauli spin operators originally proposed by Shigefumi Naka, and deduce another new bosonic representation of Pauli operators. The related coherent states, which are nonlinear coherent state and coherent spin states for two spins, respectively, are constructed.

DOI
10.1088/0253-6102/43/1/004

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Using both the fermionic-like and the bosonic-like properties of the Pauli spin operators σ + , σ − , and σ z we discuss the derivation of Bose description of the Pauli spin operators originally proposed by Shigefumi Naka, and deduce another new bosonic representation of Pauli operators. The related coherent states, which are nonlinear coherent state and coherent spin states for two spins, respectively, are constructed.
Using both the fermionic-like and the bosonic-like properties of the Pauli spin operators we discuss the Bose description of the Pauli spin operators firstly proposed by Shigefumi Naka, and derive another new bosonic representation of the Pauli spin operators. The eigenvector of σ−σ_{-}σ−​ in the bosonic representation is a nonlinear coherent state with the eigenvalues being the Grassmann numbers.
A new method of treating problems of spin systems is developed, in which spin operators are transformed into two kinds of boson operators according to Schwinger's method. Usual treatment of coherent state representation is generalized to spin systems with a fixed magnitude S . Some basic properties and the relations to the atomic coherent state are investigated rather in details. The method is applied to spin relaxation process and a corresponding Fokker-Planck type equation is obtained and solved to give a multiple relaxation process due to nonlinearities. It is shown that our formulation has several advantages over other ones in some respects.
Based on a hybrid mapping, the vector coherent state theory is revisited. The hybrid mapping of a fermion state with N coherent (collective) fermion pairs and u unpaired (noncollective) fermions leads to a hybrid state with N bosons and u fermions. The hybrid mapping is exact by which the formidable problem of finding the matrix elements of a fermion operator for a (2N+u)-fermion system is reduced to that for a u-fermion system. The Pauli effects are totally taken into account by the overlap matrix (the K matrix) for the fermion states. The application to a fermion system with the Sp(6)\ensuremath{\supset}U(3) dynamical symmetry is discussed where it is vividly seen that the occurrence of the dynamical Pauli factors is related to the fermion pair\ensuremath{\leftrightarrows}boson transformation. The intricate properties of the intrinsic operators and the K operator are discussed in detail.