标题： 旋量域壁和任意域壁上的测试费米子 显示英文标题

标题： Spinor domain wall and test fermions on an arbitrary domain wall

摘要： 我们考虑嵌入在具有非对角度规的五维时空中的旋量域壁。 得到了不同参数下线性和非线性旋量场的对应平面对称解。 结果表明，在一般情况下，度规函数和旋量场不具有相对于域壁的$Z_2$对称性。 我们研究了由于旋量场的存在而产生的域壁的角动量密度。 考虑了位于任意域壁上的测试费米子的性质。 引入了“第二自旋”（由于五维时空中的洛伦兹群生成元的性质而产生）和“第二磁场”（表示电磁场五张量的成分$F_{i 5}$）的概念。 我们找到了“第二自旋”的本征旋量，并表明其中一些代表贝尔态。 在非相对论极限下，我们推导了域壁上测试费米子的泡利方程，该方程包含一个额外项，描述自旋为$1/2$的粒子与“第二磁场”的相互作用；这使得能够实验验证额外维度的存在。 显示英文摘要

摘要： We consider a spinor domain wall embedded in a five-dimensional spacetime with a nondiagonal metric. The corresponding plane symmetric solutions for linear and nonlinear spinor fields with different parameters are obtained. It is shown that in the general case the metric functions and spinor fields do not possess $Z_2$ symmetry with respect to the domain wall. We study the angular momentum density of the domain wall arising because of the presence of the spinor field creating the wall. The properties of test fermions located on an arbitrary domain wall are considered. The concepts of the ``second spin'' (arising due to the properties of the Lorentz group generators in a five-dimensional spacetime) and of the ``second magnetic field'' (representing the components $F_{i 5}$ of the electromagnetic field five-tensor) are introduced. We find eigenspinors of the ``second spin'' and show that some of them represent the Bell states. In the nonrelativistic limit we derive the Pauli equation for the test fermions on the domain wall which contains an extra term describing the interaction of a spin-$1/2$ particle with the ``second magnetic field''; this allows the possibility of an experimental verification of the existence of extra dimensions.