Abstract
A formulation of many-body perturbation theory starting from the operator equation (H,Q+)= omega Q+ is presented. The method of solution is based on an operator scalar product, (X/Y)=Tr(X+Y), which allows the use of resolvent and partitioning techniques to establish Rayleigh-Schrodinger or Brillouin-Wigner perturbation theory for the excitation energy and excitation operator, Q+. The excitation operator contains all information about the two states involved in the transition. Specific results are given for removal or addition of an electron and for excitations of particle-hole type and comparison with the Green's function methods is made.