Generalized uncertainty principle for a Dirac fermion in a torsion field

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.

16 pages, 14 figures

References in corpus (5)

• Generalized Uncertainty Principle and Self-dual Black Holes
• A new length scale, and modified Einstein-Cartan-Dirac equations for a point mass
• Einstein-Cartan-Dirac equations in the Newman-Penrose formalism
• A duality between curvature and torsion
• A new length scale for quantum gravity