Gluon spectrum in a quark-gluon plasma under strong magnetic fields

We obtain the general expression of the gluon propagator at finite temperature ($T$) and in a magnetic field ($B$), for the case that the four transverse tensor structures appear in the gluon self-energy. By using this expression and a specific form of the one-loop gluon self-energy in the lowest Landau level approximation, we analyze the gluon spectrum in the strong magnetic field limit. As a result, we find that there exist two collective excitations of which the energies are of the order of $p\sim gT$ with $g$ being the coupling constant. One of the two excitations enjoys properties quite different from those of the collective excitations at $B=0$ which have been discussed by using the hard thermal loop approximation. We also discuss the static and dynamical screening effects, which are expected to be important for computation of transport coefficients in strong magnetic fields.