  There exist two deformations of standard electrodynamics that describe
Lorentz symmetry violation in the photon sector: CPT-odd Maxwell-Chern-Simons
theory and CPT-even modified Maxwell theory. In this article, we focus on the
parity-odd nonbirefringent sector of modified Maxwell theory. It is coupled to
a standard Dirac theory of massive spin-1/2 fermions resulting in a modified
quantum electrodynamics (QED). This theory is discussed with respect to
properties such as microcausality and unitarity, where it turns out that these
hold. Furthermore, a priori, the limit of the theory for vanishing
Lorentz-violating parameters seems to be discontinuous. Since it is not clear,
whether this is a gauge artifact, the cross section for a physical process -
modified Compton scattering - is calculated numerically. Despite the numerical
instabilities occurring for scattering of unpolarized electrons off polarized
photons in the second physical polarization state, it is shown that for
Lorentz-violating parameters much smaller than 1 the modified theory approaches
standard QED, which is strengthened by analytical investigations. Hence, the
theory proves to be consistent, at least with regard to the investigations
performed. This leads to the interesting result of having a well-defined
parity-odd extension of QED.
