https://doi.org/10.1140/epja/s10050-023-01198-y
Regular Article - Theoretical Physics
On the dynamical kernels of fermionic equations of motion in strongly-correlated media
1
Department of Physics, Western Michigan University, 1903 W Michigan Ave, 49008-5252, Kalamazoo, MI, USA
2
Facility for Rare Isotope Beams, Michigan State University, 640 S Shaw Lane, 48824, East Lansing, Michigan, USA
3
GANIL, CEA/DRF-CNRS/IN2P3, Bd Henri Becquerel, 14076, Caen, Calvados, France
Received:
15
August
2023
Accepted:
17
November
2023
Published online:
11
December
2023
Two-point fermionic propagators in strongly-correlated media are considered with an emphasis on the dynamical interaction kernels of their equations of motion (EOM). With the many-body Hamiltonian confined by a two-body interaction, the EOMs for the two-point fermionic propagators acquire the Dyson form and, before taking any approximation, the interaction kernels decompose into the static and dynamical (time-dependent) contributions. The latter translate to the energy-dependent and the former map to the energy-independent terms in the energy domain. We dwell particularly on the energy-dependent terms, which generate long-range correlations while making feedback on their short-range static counterparts. The origin, forms, and various approximations for the dynamical kernels of one-fermion and two-fermion propagators, most relevant in the intermediate-coupling regime, are discussed. Applications to the electromagnetic dipole response of Ni and low-energy quadrupole response of
Sn are presented.
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© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.