  We have established the Gupta-Bleuler quantization of the photon belonging to
the anisotropic parity-even sector of the CPT-even and Lorentz-violating
nonbirefringent electrodynamics of the standard model extension. We first
present a rule for the Maxwell electrodynamics to be successfully quantized via
Gupta-Bleuler technique in the Lorentz gauge. Recognizing the failure of the
Gupta-Bleuler method in the Lorentz gauge, $\partial _{\mu }A^{\mu }=0$, for
this massless LV theory, we argue that Gupta-Bleuler can be satisfactorily
implemented by choosing a modified Lorentz condition, $\partial _{\mu }A^{\mu
}+\kappa ^{\mu \nu }\partial _{\mu }A_{\nu }=0$, where $\kappa ^{\mu \nu }$
represents the Lorentz-violation in photon sector. By using a plane-wave
expansion for the gauge field, whose polarization vectors are determined by
solving an eigenvalue problem, and a weak Gupta-Bleuler condition, we obtain a
positive-energy Hamiltonian in terms of annihilation and creation operators.
The field commutation relation is written in terms of modified Pauli-Jordan
functions, revealing the preservation of microcausality for sufficiently small
LV parameters.
