  In the present work, we study different aspects of Lorentz and CPT symmetry
violation in extended massless QED. By following the observation that the 2+1
dimensional Maxwell-Chern-Simons theory can be originated from the 3+1
dimensional Chern-Simons-like action, we also focus on the fermion sector to
relate the 3+1 dimensional extended massless QED to 2+1 dimensional massive
QED. We take advantage of this to state that the Chern-Simons-like action in
extended massless QED can be induced with its coefficient being well defined
and finite just as its 2+1 counterpart. We make use of three different
regularization schemes by inducting the Chern-Simons-like in 3+1 dimensions to
support this conjecture.
