Premium
Self‐energy operator and self‐energy fields in many‐body systems: Liouvillian approach
Author(s) -
Bochicchio Roberto C.,
Grinberg Horacio
Publication year - 2002
Publication title -
international journal of quantum chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.484
H-Index - 105
eISSN - 1097-461X
pISSN - 0020-7608
DOI - 10.1002/qua.10097
Subject(s) - propagator , density matrix , decoupling (probability) , operator (biology) , mathematics , observable , quantum , algebraic number , mathematical physics , physics , quantum mechanics , mathematical analysis , chemistry , repressor , control engineering , transcription factor , engineering , gene , biochemistry
An explicit definition for the self‐energy field operator and the self‐energy fields obtained from an average of the associated operator within the algebraic formalism of superoperators is presented. It stems from the formal expansion of the many‐body propagator equations of motion hierachy in quantum many‐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 the interaction potential is shown. This states that the interaction potential to a given order only depends on one q ‐reduced density matrix. The contraction order q of the density matrix depends on both the nature of the operators defining the propagator and the actual order of the expansion. This result is rigorous regarding infinite summation of the irreducible terms of the self‐energy fields and provides a direct way to estimate the extent to which many‐body effects are involved in successive approximations, i.e., truncation of the excitation level given by the reference state throughout the reduced density matrix and the expansion of the propagator. © 2002 John Wiley & Sons, Inc. Int J Quantum Chem, 2002