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We calculate, in a systematic way, the general structure of the self-energyof light massive fermions and the effective propagator in a thermomagneticmedium with the inclusion of anomalous magnetic moment (AMM) of the fermion inthe weak field approximation. It is found that the self-energy of a massivefermion in this case consists of five non-trivial structure factors in contrastto the massless case where the self-energy contains only four. We employ thereal time formalism (RTF) of thermal field theory within the ambit of hardthermal loop (HTL) approximation in the evaluation of the structure factors.The collective modes are obtained from the poles of the effective propagator ofthe fermion. The investigation of the dispersion relations for non-degenerateground state shows that the effect of the magnetic field is more for up quarkthan the down quark because of the larger charge of the former. The importantobservation is that in the first excited state the degeneracy, which exists fornon-zero magnetic field is lifted due to the inclusion of the AMM. It is alsoobserved that the first excited state becomes less dispersive compared to thecase when AMM is not considered, whereas the second excited state becomes moredispersive when both the magnetic field and the AMM are non-zero in comparisonto the case with vanishing AMM. These effects are observed in both particle andhole-like excitations. Qualitatively similar behaviour is also seen in the caseof down quarks.

Collective modes of a massive fermion in a magnetized medium with finite anomalous magnetic moment