Gupta--Bleuler's quantization of the anisotropic parity-even and CPT-even electrodynamics of standard model extension
| Autor: | M. M. Ferreira, F. E. P. dos Santos, Rodolfo Casana |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2014 |
| Předmět: |
Physics
High Energy Physics - Theory Nuclear and High Energy Physics Lorentz transformation Plane wave FOS: Physical sciences Parity (physics) Physics::Classical Physics Renormalization symbols.namesake Lorenz gauge condition High Energy Physics - Theory (hep-th) Standard-Model Extension Quantum mechanics Quantum electrodynamics symbols Gauge theory Hamiltonian (quantum mechanics) |
| Popis: | We have established the Gupta-Bleuler quantization of the photon belonging to the anisotropic parity-even sector of the $CPT$-even and Lorentz-violating (LV) nonbirefringent electrodynamics of the standard model extension. We first present a rule for the Maxwell electrodynamics to be successfully quantized via the Gupta-Bleuler technique in the Lorentz gauge. Recognizing the failure of the Gupta-Bleuler method in the Lorentz gauge, ${\ensuremath{\partial}}_{\ensuremath{\mu}}{A}^{\ensuremath{\mu}}=0$, for this massless LV theory, we argue that Gupta-Bleuler can be satisfactorily implemented by choosing a modified Lorentz condition, ${\ensuremath{\partial}}_{\ensuremath{\mu}}{A}^{\ensuremath{\mu}}+{\ensuremath{\kappa}}^{\ensuremath{\mu}\ensuremath{\nu}}{\ensuremath{\partial}}_{\ensuremath{\mu}}{A}_{\ensuremath{\nu}}=0$, where ${\ensuremath{\kappa}}^{\ensuremath{\mu}\ensuremath{\nu}}$ represents the Lorentz violation in the 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. This procedure works even at second order (the birefringent regime). |
| Databáze: | OpenAIRE |
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