Abstract
We calculate a finite momentum-dependent part of the photon polarization operator in a simple model of Lorentz-violating quantum electrodynamics nonperturbatively at all orders of Lorentz-violating parameters. We sum one-particle reducible diagrams into the modified photon propagator, and determine the physical photon dispersion relation as the location of its pole. The photon dispersion relation, as well as its group velocity, acquires the one-loop momentum-dependent radiative correction. We constrain the Lorentz-violating parameters for heavy charged fermions (muon, $\tau$-lepton, top-quark) from the photon timing observations.
Highlights
Small violation of Lorentz invariance (LI) may take place in physics at low energies as a relic of some unknown ultraviolet theory, which includes quantum gravity
The aim of this article is to adopt this nonperturbative approach in the calculation of the finite momentum–dependent part of the photon polarization operator, which allows us to calculate one-loop radiative correction to the photon dispersion relation
III, we provide the one-loop calculation of the photon polarization operator, summarize one-loop radiative corrections to the photon propagator, and compute the modified photon dispersion relation
Summary
Small violation of Lorentz invariance (LI) may take place in physics at low energies as a relic of some unknown ultraviolet theory, which includes quantum gravity. Cambiaso et al [19] have calculated the momentumdependent radiative correction to the electron dispersion relation in a leading order on SME parameters in a simplified CPT-even nonbirefringent version of the SME. The aim of this article is to adopt this nonperturbative approach in the calculation of the finite momentum–dependent part of the photon polarization operator, which allows us to calculate one-loop radiative correction to the photon dispersion relation. The charge of this nonperturbative treatment is the restriction to a very limited number of LV parameters. We apply the expressions (7), (9)–(11) to compute the oneloop photon polarization operator
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