  {Following a successfully quantization scheme previously }{{% developed {\ in
Ref. \cite{GUPTAEVEN} for a}} parity-even {gauge sector} {of the SME, we}} have
established the Gupta-Bleuler {% quantization {of a} {\ parity-odd} and
CPT-even }electrodynamics of {the }standard model extension (SME) {without
recoursing to a small photon mass regulator}. {Keeping the photons massless,}
{% {we have adopted the gauge fixing condition:}} $G(A_{\mu })=(\partial
_{0}+\kappa^{0j}\partial _{j}) (A_{0}+\kappa ^{0k}A_{k})+\partial _{i}A^{i}$% .
The{\ four} polarization vectors of the gauge field are {% exactly} determined
by solving an eigenvalue problem,{\ exhibiting birefringent second order
contributions in the Lorentz-violating parameters}% . They allow to express the
Hamiltonian in terms of annihilation and creation operators whose positivity is
guaranteed by imposing a weak Gupta-Bleuler constraint, defining the physical
states. Consequently, we compute the field commutation relation which has been
expressed in terms of Pauli-Jordan functions modified by Lorentz violation
whose light-cone structures have allowed to analyze the microcausality issue.
