  We calculate, in a systematic way, the general structure of the self-energy
of light massive fermions and the effective propagator in a thermomagnetic
medium with the inclusion of anomalous magnetic moment (AMM) of the fermion in
the weak field approximation. It is found that the self-energy of a massive
fermion in this case consists of five non-trivial structure factors in contrast
to the massless case where the self-energy contains only four. We employ the
real time formalism (RTF) of thermal field theory within the ambit of hard
thermal loop (HTL) approximation in the evaluation of the structure factors.
The collective modes are obtained from the poles of the effective propagator of
the fermion. The investigation of the dispersion relations for non-degenerate
ground state shows that the effect of the magnetic field is more for up quark
than the down quark because of the larger charge of the former. The important
observation is that in the first excited state the degeneracy, which exists for
non-zero magnetic field is lifted due to the inclusion of the AMM. It is also
observed that the first excited state becomes less dispersive compared to the
case when AMM is not considered, whereas the second excited state becomes more
dispersive when both the magnetic field and the AMM are non-zero in comparison
to the case with vanishing AMM. These effects are observed in both particle and
hole-like excitations. Qualitatively similar behaviour is also seen in the case
of down quarks.
