Generalized uncertainty principle for a Dirac fermion in a torsion field

TL;DR

This paper derives a modified uncertainty principle for Dirac fermions in a torsion field, revealing corrections to the Heisenberg principle and connecting to the generalized uncertainty principle through solitary wave solutions.

Contribution

It introduces a correction factor to the Heisenberg uncertainty principle in torsion fields and derives the GUP from solutions of the Hehl-Datta equation in 1+1 dimensions.

Findings

Uncertainty relation is corrected by torsion effects.

Results align with the generalized uncertainty principle.

Probability density transformation depends on particle mass.

Abstract

We derive the uncertainty principle for a Dirac fermion in a torsion field obeying the Hehl-Datta (HD) equation. We first discuss that there should be a correction factor to the Heisenberg uncertainty principle (HUP) when torsional effects are taken into consideration. We then derive the uncertainty relation from a solitary wave solution of the HD equation in 1+1 dimensions. We find that the results agree with the generalized uncertainty principle (GUP). We then introduce the unified length scale $L_{CS}$ (which unifies Compton wavelength and Schwarzschild radius) into the HD equation and see how the probability density of the solution transforms for particles of different masses.