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 normally introduced by postulating the commutation relations $[\hat{x}^i, \hat{p}^j] = i\hbar \delta^{ij}$. However, as suggested by some quantum gravity models and string theory, this basic principle no longer holds true in the presence of a minimal length, possible the Plank length, and modifications of the commutation have been proposed i.e., of the form $[\hat{x}^\mu, \hat{p}^\nu ] = -i\hbar(1 + \beta_0 \, \hat{p}^2/\Lambda^2 )\eta^{\mu\nu}$(plus possible additional terms). In this work we will consider the previous modified uncertainty principle in terms of an effective field theory, comment upon some theoretical subtleties that are often overlooked in the literature, and constrain, for the first time, the $\Lambda$ scale with the Compton high-energy experimental data. Our findings suggest that high-energy experiments are potentially sensitive to these corrections and could serve as an effective framework for probing possible violations of the Heisenberg uncertainty principle