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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| Autores principales: | , |
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1998
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| 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 |
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| Sumario: | 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. |
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