Generalized uncertainty principle for Dirac fermion in a torsion field

We derive the uncertainty principle for a Dirac fermion in a torsion field obeying the Hehl-Datta (HD) equation. We find out how the non-linear term in the HD equation modifies the uncertainty principle and how it compares with the generalized uncertainty principle (GUP). 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 then introduce the unified length scale LCS (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.