  Theories of Quantum Gravity predict a minimum measurable length and a
corresponding modification of the Heisenberg Uncertainty Principle to the
so-called Generalized Uncertainty Principle (GUP). However, this modification
is usually formulated in non-relativistic language, making it unclear whether
the minimum length is Lorentz invariant. We have formulated a Relativistic
Generalized Uncertainty Principle, resulting in a Lorentz invariant minimum
measurable length and the resolution of the composition law problem. This
proved to be an important step in the formulation of Quantum Field Theory with
minimum length. We derived the Lagrangians consistent with the existence of
minimal length and describing the behaviour of scalar, spinor, and U(1) gauge
fields. We calculated the Feynman rules (propagators and vertices) associated
with these Lagrangians. Furthermore, we calculated the Quantum Gravity
corrected scattering cross-sections for a lepton-lepton scattering. Finally, we
compared our results with current experiments, which allowed us to improve the
bounds on the scale at which quantum gravity phenomena will become relevant.
