Abstract Recently, the authors presented a covariant extension of the Generalized Uncertainty Principle (GUP) with a Lorentz invariant minimum length. This opens the way for constructing and exploring the observable consequences of minimum length in Relativistic Quantum Field Theories. In particular, we compute quantum gravity corrections to high energy scattering experiments, which may provide the much needed window of testing minimum length and quantum gravity theories in the laboratory. To this end, we formulate the Lagrangian of Quantum Electrodynamics for a complex scalar fields from the GUP modified minimally coupled Klein-Gordon equation and write down its Feynman rules. We then calculate the Relativistic Generalized Uncertainty Principle corrections to a Quantum Electrodynamics scattering amplitude and discuss its implications.

中文翻译：

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具有广义不确定性原理的量子场论 I：标量电动力学

摘要 最近，作者提出了具有洛伦兹不变最小长度的广义不确定性原理 (GUP) 的协变扩展。这为构建和探索相对论量子场论中最小长度的可观察结果开辟了道路。特别是，我们计算了对高能散射实验的量子引力校正，这可能为在实验室中测试最小长度和量子引力理论提供急需的窗口。为此，我们从 GUP 修正的最小耦合 Klein-Gordon 方程为复杂标量场制定了量子电动力学的拉格朗日量，并写下了其费曼规则。然后，我们计算相对论广义不确定性原理对量子电动力学散射幅度的修正并讨论其含义。