  We calculate gluon self-energy using quark energy projectors in a general
quark-gluon plasma. By separating the quark field into a positive- and a
negative-energy mode, the quark loop constructed with the same mode is always
convergent, and the divergence appears only in the mixed loop with different
modes and is medium independent. After removing the divergence in vacuum, we
obtain the one-loop gluon self-energy at finite temperature, chemical potential
and quarks mass without approximation. With the method of quark loop
resummation, we calculate non-perturbatively the gluon Debye mass and
thermodynamic potential. In the limit of small gluon momentum in comparison
with temperature, chemical potential and quark mass, our calculation comes back
to the known HTL/HDL results in literature.
