标题： 二维超曲面上狄拉克费米子的一般协变几何动量和几何势 显示英文标题

标题： Generally covariant geometric momentum and geometric potential for a Dirac fermion on a two-dimensional hypersurface

摘要： 几何动量是约束在弯曲表面上运动粒子的适当动量，它依赖于外曲率并具有可观测效应。 在多组分量子态的背景下，几何动量应被重写为普遍协变的几何动量。 对于约束在二维超曲面上的狄拉克费米子，我们给出了普遍协变的几何动量，并表明在伪球面和螺旋面上不存在由曲率引起的几何势。 这些结果验证了动力学量子化条件在处理超曲面上约束系统时的有效性，人们可以得到约束在具有明确参数方程的表面上的自旋粒子的普遍协变几何动量和几何势。 显示英文摘要

摘要： Geometric momentum is the proper momentum for a moving particle constrained on a curved surface, which depends on the outer curvature and has observable effects. In the context of multi-component quantum states, geometric momentum should be rewritten as generally covariant geometric momentum. For a Dirac fermion constrained on a two-dimensional hypersurface, we give the generally covariant geometric momentum, and show that on the pseudosphere and the helical surface there exist no curvature-induced geometric potentials. These results verify that the dynamical quantization conditions are effective in dealing with constrained systems on hypersurfaces, and one could obtain the generally convariant geometric momentum and the geometric potential of a spin particle constrained on surfaces with definite parametric equations.