  The dilepton production by the constituents of the strongly interacting
quark-gluon-plasma (sQGP) is addressed. In order to make quantitative
predictions at realistically low plasma temperatures (O(T_c)), experimentally
relevant low dilepton mass (O(1 GeV)) and strong coupling (alphaS=0.5-1), we
take into account not only the higher order pQCD reaction mechanisms, but also
the non-perturbative spectral functions (off-shellness) and self-energies of
the quarks, anti-quarks and gluons thus going beyond the leading twist. For
this purpose, our calculations utilize parametrizations of the non-perturbative
propagators for quarks and gluons provided by the dynamical quasi-particle
model (DQPM) matched to reproduce lattice data. The DQPM describes QCD
properties in terms of single-particle Green's functions (in the sense of a
two-particle irreducible approach) and leads to the notion of the constituents
of the sQGP being effective quasiparticles, which are massive and have broad
spectral functions (due to large interaction rates). In the present work, we
derive the off-shell cross sections of dilepton production in the reactions
q+qbar->l^+l^- (Drell-Yan mechanism), q+qbar->g+l^+l^- (quark annihilation with
the gluon Bremsstrahlung in the final state), q(qbar)+g->q(qbar)+l^+l^- (gluon
Compton scattering), g->q+qbar+l^+l^- and q(qbar)->q(qbar)+g+l^+l^- (virtual
gluon decay, virtual quark decay) in the sQGP by dressing the quark and gluon
lines in the perturbative diagrams with the DQPM propagators for quarks and
gluons.
