On the dynamical kernels of fermionic equations of motion in strongly-correlated media

TL;DR

This paper analyzes the energy-dependent dynamical kernels in fermionic equations of motion within strongly-correlated media, highlighting their role in long-range correlations and feedback effects, with applications to nuclear electromagnetic and quadrupole responses.

Contribution

It provides a detailed examination of the origin, forms, and approximations of dynamical kernels in fermionic propagators, especially in the intermediate-coupling regime, with practical nuclear physics applications.

Findings

Dynamical kernels generate long-range correlations.

Feedback effects influence short-range static kernels.

Applications demonstrate relevance to nuclear electromagnetic and quadrupole responses.

Abstract

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 $^{68,70}$Ni and low-energy quadrupole response of $^{114,116,124}$Sn are presented.