On a new formulation of the continuum Heisenberg spin system in a space of arbitrary dimensionality

Abstract

The classical equations of motion of a continuum Heisenberg spin system in N dimensions are written in the form of equations for a particle field and a gauge field. Known results, such as the exact solution for N = 1 and the self-dual solution for N = 2, are recovered. Of the new results we mention: (a) velocity independence of the soliton-energy for N = 1; (b) equivalence with a nonlinear Schrödinger equation in N dimensions; (c) relation to the static sine-Gordon equation; (d) numerical calculations of finite-energy solutions in two and three dimensions.