  According to the dynamical quasiparticle model (DQPM) -- matched to reproduce
lattice QCD results in thermodynamic limit, -- the constituents of the strongly
interacting quark-gluon plasma (sQGP) are massive and off-shell quasi-particles
(quarks and gluons) with broad spectral functions. In order to address the
electromagnetic radiation of the sQGP, we derive off-shell cross sections of
$q\bar q\to\gamma^*$, $q\bar q\to\gamma^*+g$ and $qg\to\gamma^*q$($\bar q
g\to\gamma^* \bar q$) reactions taking into account the effective propagators
for quarks and gluons from the DQPM. Dilepton production in In+In collisions at
158 AGeV is studied by implementing these processes into the
parton-hadron-string dynamics (PHSD) transport approach. The microscopic PHSD
transport approach describes the full evolution of the heavy-ion collision:
from the dynamics of quasi-particles in the sQGP phase (when the local energy
density is above $\sim 1$ GeV/fm$^3$) through hadronization and to the
following hadron interactions and off-shell propagation after the
hadronization. A comparison to the data of the NA60 Collaboration shows that
the low mass dilepton spectra are well described by including a collisional
broadening of vector mesons, while the spectra in the intermediate mass range
are dominated by off-shell quark-antiquark annihilation, quark Bremsstrahlung
and gluon-Compton scattering in the nonperturbative QGP. In particular, the
observed softening of the $m_T$ spectra at intermediate masses (1 GeV $\le M
\le$ 3 GeV) is approximately reproduced.
