Grigory Rubtsov, Petr Satunin, Sergey Sibiryakov
We show that violation of the Lorentz symmetry in quantum electrodynamics can suppress the rates of the interactions crucial for the formation of photon-induced air showers, such as pair production on nuclei and in the geomagnetic field. As a consequence, the allowed region in the space of Lorentz-violating parameters will be seriously restricted if several photons with energies $\gtrsim\,10^{19}\, {eV}$ are detected.
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http://arxiv.org/abs/1307.8027
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