We consider the problem of having relativistic quantum mechanics re-formulated with hydrodynamic variables, and specifically the problem of deriving the Mathisson–Papapetrou–Dixon equations (describing the motion of a massive spinning body moving in a gravitational field) from the Dirac equation. The problem will be answered on a general manifold with torsion and gravity. We will demonstrate that when plane waves are considered the MPD equations describe the general relativistic wave-particle duality with torsion (Guedes and Popławski 2024 Class. Quantum Grav. 41 065011), but we will also see that in such a form the MPD equations become trivial.

中文翻译：

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扭转引力中旋量场的经典特性


我们考虑了用流体动力学变量重新表述相对论量子力学的问题，特别是从狄拉克方程推导出 Mathisson-Papapetrou-Dixon 方程（描述在引力场中运动的大质量旋转体的运动）的问题。这个问题将在具有扭转和重力的一般流形上得到解答。我们将证明，当考虑平面波时，MPD 方程描述了具有扭转作用的广义相对论波粒二象性（Guedes 和 Popławski 2024 Class. Quantum Grav.41 065011），但我们也将看到，在这种形式下，MPD 方程变得微不足道。