  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.
