su(2) spin s representations via CP2s sigma models*

Abstract

Abstract We establish and analyze a new relationship between the matrix functions describing spin fields of a spin s, where 2 s ∈ Z + , and C P 2 s two-dimensional Euclidean sigma models. The spin matrices are constructed from the rank-1 Hermitian projectors of the sigma models or from the anti-Hermitian immersion functions of their soliton surfaces in the su ( 2 s + 1 ) algebra. We provide a geometric interpretation of this construction. For the spin fields which can be represented as linear combinations of the generalized Pauli matrices, we find the dynamics equation satisfied by their coefficients. This equation is identical to the stationary equation of a two-dimensional Heisenberg model. We show that the same holds for matrices congruent to the generalized Pauli matrices through any coordinate-independent unitary linear transformation. These properties allow for new interpretations of the spins as compositions of more elementary objects. They also open up the possibility of future applications of the sigma models to the situations which depend on spin behaviour, including spintronics, spin glasses and quantum computing.