Dynamical symmetry approach to many-body systems

Full text: We present a novel method to study quantum many-body systems which can be mapped on an effective spin system. The method is based on path integral formulation of the theory. We make use of the dynamical symmetry of the Hamiltonian and we convert the path integrals into a set of stochastic differential equations or, equivalently, to a Fokker-Planck equation. For particular cases, the quantities of interest can be evaluated explicitly, while in general our formulation serves as a good starting point for various approximation schemes. We demonstrate the method on the problem of multiple-photon scattering on an atom and on the problem of spin diffusion. (author)