  The fundamental physical description of the Universe is based on two
theories: Quantum Mechanics and General Relativity. Unified theory of Quantum
Gravity (QG) is an open problem. Quantum Gravity Phenomenology (QGP) studies QG
effects in low-energy systems. The basis of one such phenomenological model is
the Generalized Uncertainty Principle (GUP), which is a modified Heisenberg
uncertainty relation and predicts a deformed position-momentum commutator.
  Relativistic Generalized Uncertainty Principle (RGUP) is proposed in this
thesis, which gives a Loerentz invariant minimum length and resolves the
composition law problem. RGUP modified Klein-Gordon, Schrodinger and Dirac
equations with QG corrections to several systems are presented. The Lagrangians
of Quantum Electrodynamics for the gauge, scalar, and spinor fields are
obtained. The RGUP corrections to scattering amplitudes are then calculated.
The results are applied to high energy scattering experiments providing much
needed window for testing minimum length and QG theories in the laboratory.
