Algebraic relations between Dyson and Liouvillian self-energy field approaches

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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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Autores principales: Bochicchio, Roberto Carlos, Grinberg, Horacio
Publicado: 1998
Materias:
Dyson equation
Equation of motion
Liouvillian self-energies
Propagators
Acceso en línea:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_01661280_v426_n1-3_p9_Bochicchio
http://hdl.handle.net/20.500.12110/paper_01661280_v426_n1-3_p9_Bochicchio
Aporte de:
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
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spelling paper:paper_01661280_v426_n1-3_p9_Bochicchio2023-06-08T15:15:18Z Algebraic relations between Dyson and Liouvillian self-energy field approaches Bochicchio, Roberto Carlos Grinberg, Horacio 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. 1998 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_01661280_v426_n1-3_p9_Bochicchio 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, Roberto Carlos
Grinberg, Horacio
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.
author Bochicchio, Roberto Carlos
Grinberg, Horacio
author_facet Bochicchio, Roberto Carlos
Grinberg, Horacio
author_sort Bochicchio, Roberto Carlos
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
publishDate 1998
url https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_01661280_v426_n1-3_p9_Bochicchio
http://hdl.handle.net/20.500.12110/paper_01661280_v426_n1-3_p9_Bochicchio
work_keys_str_mv AT bochicchiorobertocarlos algebraicrelationsbetweendysonandliouvillianselfenergyfieldapproaches
AT grinberghoracio algebraicrelationsbetweendysonandliouvillianselfenergyfieldapproaches
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