The Generalized Uncertainty Principle. New Bounds and Trends

Abstract The Heisenberg uncertainty principle is one of the fundamental pillars of quantum mechanics and quantum field theory. It is usually introduced through the canonical commutation relations 
\(
[\hat{x}^i,\hat{p}^j] = i\hbar \delta^{ij}.
\)
Several approaches to quantum gravity and string theory suggest that this relation may be modified in the presence of a minimal length scale, possibly of the order of the Planck length, leading to generalized uncertainty principle (GUP) scenarios. In this work we investigate the phenomenological consequences of a class of GUP-inspired deformations characterized by modified the Heisenberg commutation relations.

Our analysis is carried out within an effective field-theory framework and focuses on the leading-order corrections induced by the deformation parameter. Using high-energy Compton scattering data, we derive, for the first time, bounds on the characteristic scale \(\Lambda\) controlling these deformations. Our results indicate that high-energy experiments may be sensitive to such corrections and provide a phenomenological avenue to probe possible minimal-length effects beyond standard quantum mechanics.