Discreteness of Space from GUP II: Relativistic Wave Equations

Understand

Various theories of Quantum Gravity predict modifications of the Heisenberg Uncertainty Principle near the Planck scale to a so-called Generalized Uncertainty Principle (GUP).

• In some recent papers, we showed that the GUP gives rise to corrections to the Schrodinger equation, which in turn affect all quantum mechanical Hamiltonians.
• In particular, by applying it to a particle in a one dimensional box, we showed that the box length must be quantized in terms of a fundamental length (which could be the Planck length), which we interpreted as a signal of fundamental discreteness of space itself.
• In this paper, we extend the above results to a relativistic particle in a rectangular as well as a spherical box, by solving the GUP-corrected Klein-Gordon and Dirac equations, and for the latter, to two and three dimensions.