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.

中文翻译：

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扭转场中狄拉克费米子的广义不确定性原理

我们推导出服从 Hehl-Datta (HD) 方程的扭转场中狄拉克费米子的不确定原理。我们首先讨论当考虑扭转效应时，海森堡不确定性原理（HUP）应该有一个修正因子。然后我们从 1+1 维 HD 方程的孤立波解中推导出不确定性关系。我们发现结果与广义不确定性原理（GUP）一致。然后，我们将统一长度尺度 $L_{CS}$（统一康普顿波长和施瓦西半径）引入 HD 方程，并查看解的概率密度如何针对不同质量的粒子进行变换。