Noncommutative Electrodynamics and Ultra High Energy Gamma Rays

Plane waves in noncommutative classical electrodynamics (NCED) have a peculiar dispersion relation. We investigate the kinematical conditions on this deformed ”mass shell” which come from ultra high energy gamma rays and discuss noncommutative dynamical effects on the gamma absorption by the infrared background and on the intrinsic spectrum. Finally we note that in NCED there is a strong correlation between the modified dispersion relation and the presence of dynamical effects in electromagnetic phenomena such as in the case of the synchrotron radiation. From this point of view, the limits on the typical energy scale of the violation of Lorentz invariance obtained by deformed dispersion relations and by assuming undeformed dynamical effects should be taken with some caution. PACS numbers: 11.10.Nx 95.85.Pw 96.40-z Recently there has been a growing interest in theories where the speed of light is different from c [1]. The main motivations of considering this ’heresy’ come from cosmology, quantum gravity and observation and indeed, ultra high energy cosmic (UHECR) and gamma (UHEGR) rays have been detected with energies which seem to be inconsistent with the standard GZK cutoff [2]. It has been suggested that a possible explanation of the observed high energy cosmic rays could be a modified dispersion relation among energy, momentum and mass due to physical phenomena at Plank scale [3, 4, 5, 6, 7, 8] or to explicit Lorentz invariant breaking terms in the lagrangian, originally proposed in [9] and reconsidered more recently in [10]. Also in noncommutative electrodynamics (NCED) [11] one has a modified dispersion relation for the electromagnetic waves and in this brief note we address the question whether it is compatible with the experimental data on UHEGR and we discuss some noncommutative dynamical effects in gamma rays absorption by the diffuse interstellar or intergalactic infrared radiation and in the TeV photon intrinsic production spectrum. The simplest case of NCED is described by the action (the fermionic field is omitted):