The role of spin in the development of coherent structures in many-body systems

Abstract

Spin components have been explicitly included in an accurate analytical approach for the study of coherent structures in many-body systems. Equations of motion for annihilators and creators are transformed into non-linear equations of motion for a spin-dependent quantum field. It is demonstrated, using commutation relations for the quantum field operators, that spin-up, ψ +, and spin-down, ψ -, fields may be decoupled. The equation of motion for ψ + is shown to have a form identical to the equation of motion for ψ - which, in turn, is equivalent to that for a field with no specific spin component. The latter equations have the same form for both bosons and fermions.