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The propagation of photons, electrons and positrons at ultra-high energies above 10^{19} eV can be changed considerably if the dispersion relations of these particles are modified by terms suppressed by powers of the Planck scale. We recently pointed out that the current non-observation of photons in the ultra-high energy cosmic ray flux at such energies can put strong constraints on such modified dispersion relations. In the present work we generalize these constraints to all three Lorentz invariance breaking parameters that can occur in the dispersion relations for photons, electrons and positrons at first and second order suppression with the Planck scale. We also show how the excluded regions in these three-dimensional parameter ranges would be extended if ultra-high energy photons were detected in the future.
Lorentz symmetry breaking at very high energies may lead to photon dispersion relations of the form omega^2=k^2+xi_n k^2(k/M_Pl)^n with new terms suppressed by a power n of the Planck mass M_Pl. We show that first and second order terms of size xi_1
There has been much interest in possible violations of Lorentz invariance, particularly motivated by quantum gravity theories. It has been suggested that a small amount of Lorentz invariance violation (LIV) could turn off photomeson interactions of u
The Large High Altitude Air Shower Observatory~(LHAASO) is one of the most sensitive gamma-ray detector arrays currently operating at TeV and PeV energies. Recently the LHAASO experiment detected ultra-high-energy~(UHE; $E_{gamma}gtrsim 100~mathrm{Te
A general framework for tests of Lorentz invariance with electromagnetic waves is presented, allowing for operators of arbitrary mass dimension. Signatures of Lorentz violations include vacuum birefringence, vacuum dispersion, and anisotropies. Sensi
All quadratic translation- and gauge-invariant photon operators for Lorentz breakdown are included into the Stueckelberg Lagrangian for massive photons in a generalized xi-gauge. The corresponding dispersion relation and tree-level propagator are det