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.

References in corpus (11)

• Electrodynamics with Lorentz-violating operators of arbitrary dimension
• Matter-gravity couplings and Lorentz violation
• Sensitive polarimetric search for relativity violations in gamma-ray bursts
• Consistency of isotropic modified Maxwell theory: Microcausality and unitarity
• Limits on isotropic Lorentz violation in QED from collider physics
• Causality and stability for Lorentz-CPT violating electrodynamics with dimension-5 operators
• Eliminating the CPT-Odd f Coefficient from the Lorentz-Violating Standard Model Extension
• Feynman propagator for the nonbirefringent CPT-even electrodynamics of the Standard Model Extension
• Non-local on-shell field redefinition for the SME
• Finite Temperature behavior of the CPT-even and parity-even electrodynamics of the Standard Model Extension
• Covariant Quantization of Lorentz-Violating Electromagnetism

Cited by in corpus (3)

• A relativistic quantum oscillator subject to a Coulomb-type potential induced by effects of the violation of the Lorentz symmetry
• Field sources in a CPT-even Lorentz-violation Maxwell electrodynamics
• Gupta-Bleuler's quantization of a parity-odd CPT-even electrodynamics of the standard model extension