Self-energy operator and self-energy fields in many-body stystems:liouvillian approach

摘要

Anexplicit definition for the self-energy field operator and the self-energy fields obtained from an average of the associated operator within the algebraic fomalism of superoperators is presented.It stems from t he formal expansiono f the many-body propagator equatins of motion hierachy in quantumamny-body systems within the scenario of the Liouvillian decoupling scheme developed in previous works.An essential theoretical property of such fields for the complete expansion of the propagator to any order in theinteractionpotential is shown.This states that the interaction potential to a givenorder only depends on one q-redeuced densitymatrix.The contraction order q of the density matrix depends on both the nature of theoperators defining the propagator and the actualorder of the expansion.This result is rigorous regarding infinite summation of the ireducible termsof the self-energy fields and provides a direct way to estimate the extentto whcih many-body effects are involvedin successive approximations,i.e.,truncation of the excitation level givenby the refernce state throughout the reduced density matrix and the expansionof the propagator.