Spin-Field Correspondence

In the recent article Phys.\ Lett.\ B {\bf 759} (2016) 424 a new class of field theories called Nonlinear Field Space Theory has been proposed. In this approach, the standard field theories are considered as linear approximations to some more general theories characterized by nonlinear field phase spaces. The case of spherical geometry is especially interesting due to its relation with the spin physics. Here, we explore this possibility showing that classical scalar field theory with such a field space can be viewed as a perturbation of a continuous spin system. In this picture, the spin precession and the scalar field excitations are dual descriptions of the same physics. The duality is studied on the example of the Heisenberg model. It is shown that the Heisenberg model coupled to a magnetic field leads to a non-relativistic scalar field theory, characterized by quadratic dispersion relation. Finally, on the basis of analysis of the relation between the spin phase space and the scalar field theory we propose the \emph{Spin-Field correspondence} between the known types of fields and the corresponding spin systems.