Gupta--Bleuler's quantization of the anisotropic parity-even and CPT-even electrodynamics of standard model extension

Abstract

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.

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• From classical Lagrangians to Hamilton operators in the Standard-Model Extension
• Field sources in a CPT-even Lorentz-violation Maxwell electrodynamics
• Non-orthogonality and $\kappa$-dependence eccentricity of polarized electromagnetic waves in CPT-even Lorentz violation
• Gupta-Bleuler's quantization of a parity-odd CPT-even electrodynamics of the standard model extension
• He-McKellar-Wilkens-type effect from the Lorentz symmetry breaking effects
• The self-dual Lorentz violating model: quantization, scattering and dual equivalence
• One-loop contributions in Lorentz-violating scalar QED with nonminimal coupling