Algebraic relations between Dyson and Liouvillian self-energy field approaches
Through the superoperator algebraic formalism it is shown that Liouvillian self-energies derived from the equations of motion hierarchy for two-time propagators in stationary states of time independent Hamiltonians of N-particle systems are closely related to those obtained from the solution of the...
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todo:paper_01661280_v426_n1-3_p9_Bochicchio2023-10-03T15:03:24Z Algebraic relations between Dyson and Liouvillian self-energy field approaches Bochicchio, R.C. Grinberg, H. Dyson equation Equation of motion Liouvillian self-energies Propagators Through the superoperator algebraic formalism it is shown that Liouvillian self-energies derived from the equations of motion hierarchy for two-time propagators in stationary states of time independent Hamiltonians of N-particle systems are closely related to those obtained from the solution of the super-operator approach to Dyson equations (Dyson self-energies). It probes the quasi-equivalence of the two formulae, namely, they are equivalent to lower orders in the perturbative series expansion, a result valid for any kind of reference state used in the evaluation of the propagators leading to the self-energy fields. The relations obtained for the one-particle propagator are generalized to p-particle propagators (p < N). Thus, it shows the existence, as in the case of one-particle propagators, of Dyson like equations and consequently that the Liouvillian formulation is adequate to solve the decoupling problem in many-body physics allowing extensions to be made to other related fields such as the solution of the reduced Liouville quantum equation. © 1998 Elsevier Science B.V. Fil:Bochicchio, R.C. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. Fil:Grinberg, H. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_01661280_v426_n1-3_p9_Bochicchio |
| institution |
Universidad de Buenos Aires |
| institution_str |
I-28 |
| repository_str |
R-134 |
| collection |
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) |
| topic |
Dyson equation Equation of motion Liouvillian self-energies Propagators |
| spellingShingle |
Dyson equation Equation of motion Liouvillian self-energies Propagators Bochicchio, R.C. Grinberg, H. Algebraic relations between Dyson and Liouvillian self-energy field approaches |
| topic_facet |
Dyson equation Equation of motion Liouvillian self-energies Propagators |
| description |
Through the superoperator algebraic formalism it is shown that Liouvillian self-energies derived from the equations of motion hierarchy for two-time propagators in stationary states of time independent Hamiltonians of N-particle systems are closely related to those obtained from the solution of the super-operator approach to Dyson equations (Dyson self-energies). It probes the quasi-equivalence of the two formulae, namely, they are equivalent to lower orders in the perturbative series expansion, a result valid for any kind of reference state used in the evaluation of the propagators leading to the self-energy fields. The relations obtained for the one-particle propagator are generalized to p-particle propagators (p < N). Thus, it shows the existence, as in the case of one-particle propagators, of Dyson like equations and consequently that the Liouvillian formulation is adequate to solve the decoupling problem in many-body physics allowing extensions to be made to other related fields such as the solution of the reduced Liouville quantum equation. © 1998 Elsevier Science B.V. |
| format |
JOUR |
| author |
Bochicchio, R.C. Grinberg, H. |
| author_facet |
Bochicchio, R.C. Grinberg, H. |
| author_sort |
Bochicchio, R.C. |
| title |
Algebraic relations between Dyson and Liouvillian self-energy field approaches |
| title_short |
Algebraic relations between Dyson and Liouvillian self-energy field approaches |
| title_full |
Algebraic relations between Dyson and Liouvillian self-energy field approaches |
| title_fullStr |
Algebraic relations between Dyson and Liouvillian self-energy field approaches |
| title_full_unstemmed |
Algebraic relations between Dyson and Liouvillian self-energy field approaches |
| title_sort |
algebraic relations between dyson and liouvillian self-energy field approaches |
| url |
http://hdl.handle.net/20.500.12110/paper_01661280_v426_n1-3_p9_Bochicchio |
| work_keys_str_mv |
AT bochicchiorc algebraicrelationsbetweendysonandliouvillianselfenergyfieldapproaches AT grinbergh algebraicrelationsbetweendysonandliouvillianselfenergyfieldapproaches |
| _version_ |
1807315132643016704 |