Quantum Gravity Phenomenology from the Generalized Uncertainty Principle

The fundamental physical description of Nature is based on two mutually incompatible theories: Quantum Mechanics and General Relativity. Their unification into a theory of Quantum Gravity (QG) remains one of the main challenges of theoretical physics. A common feature of candidate theories of QG is the existence of a minimal observable length of the order of the Planck length. This prediction, though, is in contradiction with Heisenberg’s Uncertainty Principle. In fact, according to this principle it is possible to observe any length while increasing the uncertainty in momentum. In the context of Quantum Gravity Phenomenology, that studies QG effects in low-energy systems, Heisenberg’s principle is then modified into the Generalized Uncertainty Principle (GUP). GUP then imposes a minimal uncertainty in position and predicts a deformed commutation relation between position and momentum. In this talk, after introducing the basics of the Uncertainty Principle, I will show how the GUP can change known aspects of standard Quantum Mechanics, leading to ways to test theories of QG.