Generalized uncertainty principle from the regularized self-energy

Abstract

We use the Schrödinger–Newton equation to calculate the regularized self-energy of a particle using a regular self-gravitational and electrostatic potential derived in string T-duality. The particle mass M is no longer concentrated into a point but is diluted and described by a quantum-corrected smeared energy density resulting in corrections to the energy of the particle, which is interpreted as a regularized self-energy. We extend our results and find corrections to the relativistic particles using the Klein–Gordon, Proca and Dirac equations. An important finding is that we extract a form of the generalized uncertainty principle (GUP) from the corrected energy. This form of the GUP is shown to depend on the nature of particles; namely, for bosons (spin 0 and spin 1) we obtain a quadratic form of the GUP, while for fermions (spin 1/2) we obtain a linear form. The correlation we find between spin and GUP may offer insights for investigating quantum gravity.