We analyze the kinematics of electron-positron production in a photon-photon interaction when one has a modification of the special relativistic kinematics as a power expansion in the inverse of a new high-energy scale. We derive the equation for the threshold energy of this reaction to first order in this expansion, including the effects due to a modification of the energy-momentum conservation equation. In contrast with the Lorentz invariance violation case, a scale of the order of a few TeV is found to be compatible with the observations of very high-energy cosmic gamma rays in the case of a modification compatible with the relativity principle.

中文翻译：

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从宇宙透明度物理学看相对论变形运动学的界限

我们分析了光子 - 光子相互作用中电子 - 正电子产生的运动学，当一个人将特殊的相对论运动学修改为新高能标度的逆功率扩展时。我们推导出该反应的一阶阈值能量方程，包括由于能量-动量守恒方程的修改而产生的影响。与洛伦兹不变性违反情况相反，在与相对性原理兼容的修改情况下，发现几个 TeV 数量级的尺度与对极高能量宇宙伽马射线的观测相容。