弹击Dirac粒子：MIT边界条件与Thomas进动的相容性
Bouncing Dirac particles: compatibility between MIT boundary conditions and Thomas precession
摘要：
我们考虑的反射的狄拉克平面波的手征MIT边界条件所描述的完美反射平面上，并确定旋转的自旋波的反射分量。我们用托马斯旋进定义的自旋演化解了经典粒子的类似问题，并与量子结果作了比较。我们发现，在这两个问题中的自旋旋转轴重合的手征角消失，在这种情况下，旋转角重合的非相对论性的限制，也保持非常接近的相对论制度。结果表明，在非相对论极限下，自旋与非手征边界条件反射面之间的相互作用完全包含在Thomas进动效应中，这与这些边界条件等价于边界外的无限排斥标量势的事实是一致的。相比之下，在超相对论极限下，量子问题中的旋转角仍然是有限的，而在经典问题中，旋转角发散。我们评论这种差异的有效性的Mathisson-Papapetrou-Dixon方程在大加速度的可能影响。
英文摘要：
We consider the reflection of a Dirac plane wave on a perfectly reflecting plane described by chiral MIT boundary conditions and determine the rotation of the spin in the reflected component of the wave. We solve the analogous problem for a classical particle using the evolution of the spin defined by the Thomas precession and make a comparison with the quantum result. We find that the rotation axes of the spin in the two problems coincide only for a vanishing chiral angle, in which case the rotation angles coincide in the nonrelativistic limit, and also remain remarkably close in the relativistic regime. The result shows that in the nonrelativistic limit the interaction between the spin and a reflecting surface with nonchiral boundary conditions is completely contained in the Thomas precession effect, in conformity with the fact that these boundary conditions are equivalent to an infinite repulsive scalar potential outside the boundary. By contrast, in the ultrarelativistic limit the rotation angle in the quantum problem remains finite, while in the classical one the rotation angle diverges. We comment on the possible implications of this discrepancy on the validity of the Mathisson-Papapetrou-Dixon equations at large accelerations.
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