论文标题
一般性的波浪$ - $粒子双重性与扭转
General-relativistic wave$-$particle duality with torsion
论文作者
论文摘要
我们建议，狄拉克粒子的四速度与$ u^i = \barψγ^iψ/\ bar单ψ$相对论的波函数有关。对于与平面时空相关的自由粒子，证明了这种相对论波$ - $粒子二元性关系。对于带有扭转的弯曲时空，旋转器的动量四载体与交换衍生物给出的翻译产生者有关。旋转旋转器的旋转角动量四量与洛伦兹组的旋转发生器有关。在Einstein $ - $ cartan扭转的情况下，我们将旋转和能量$ - $动量张量用于旋转和能量$ - $ $ - $ - $ cartan扭转，以表明，如果波浪满足弯曲的dirac方程，则可以满足四效性，四摩尔植物，然后满足经典的Mathisson $ papapapeTrou eormitions Motion of Motion的运动。我们表明，这些方程将减少到测量方程。因此，在飞行器波量子力学中以四速度引导的粒子的运动与时空确定的大地运动运动相吻合。我们还展示了Mathisson $ - $ papapetou方程的二元性和操作员形式是如何在扭转存在下的协方差运动方程式产生的。
We propose that the four-velocity of a Dirac particle is related to its relativistic wave function by $u^i=\barψγ^iψ/\barψψ$. This relativistic wave$-$particle duality relation is demonstrated for a free particle related to a plane wave in a flat spacetime. For a curved spacetime with torsion, the momentum four-vector of a spinor is related to a generator of translation, given by a covariant derivative. The spin angular momentum four-tensor of a spinor is related to a generator of rotation in the Lorentz group. We use the covariant conservation laws for the spin and energy$-$momentum tensors for a spinor field in the presence of the Einstein$-$Cartan torsion to show that if the wave satisfies the curved Dirac equation, then the four-velocity, four-momentum, and spin satisfy the classical Mathisson$-$Papapetrou equations of motion. We show that these equations reduce to the geodesic equation. Consequently, the motion of a particle guided by the four-velocity in the pilot-wave quantum mechanics coincides with the geodesic motion determined by spacetime. We also show how the duality and the operator form of the Mathisson$-$Papapetrou equations arise from the covariant Heisenberg equation of motion in the presence of torsion.
