  We calculate the quark self-energy in a quark-gluon plasma that possesses an
ellipsoidal momentum-space anisotropy in the local rest frame. By introducing
additional transverse momentum anisotropy parameters into the parton
distribution functions, we generalize previous results which were obtained for
the case of a spheroidal anisotropy. Our results demonstrate that the presence
of anisotropies in the transverse directions affects the real and imaginary
parts of quark self-energy and, consequently, the self-energy depends on both
the polar and azimuthal angles in the local rest frame of the matter. Our
results for the quark self-energy set the stage for the calculation of the
effects of ellipsoidal momentum-space anisotropy on quark-gluon plasma photon
spectra and collective flow.
