关于盒子中一维Weyl-Majorana粒子的边界条件
On the boundary conditions for the 1D Weyl-Majorana particle in a box
摘要：
在（1+1）维时空中，我们可以同时有两个粒子，即Weyl粒子和Majorana粒子--一维Weyl-Majorana粒子。也就是说，满足马约拉纳条件的两分量狄拉克波函数的右手征和左手征部分，在外尔表示中，描述了这些粒子，并且每个都满足自己的马约拉纳条件。自然地，这两个双分量波函数中的每一个的非零分量满足外尔方程。我们调查和讨论这个问题，并证明，一维Weyl-Majorana粒子在一个盒子中，非零组件，因此手征波函数，只承认周期和反周期的边界条件。从后两个边界条件出发，我们只能构造出四个完整狄拉克波函数的边界条件。然后，我们证明，这四个边界条件也包括在最一般的一组自伴边界条件的一维马约拉纳粒子在一个盒子。
英文摘要：
In (1+1) space-time dimensions, we can have two particles that are Weyl and Majorana particles at the same time---1D Weyl-Majorana particles. That is, the right-chiral and left-chiral parts of the two-component Dirac wave function that satisfies the Majorana condition, in the Weyl representation, describe these particles, and each satisfies their own Majorana condition. Naturally, the nonzero component of each of these two two-component wave functions satisfies a Weyl equation. We investigate and discuss this issue and demonstrate that for a 1D Weyl-Majorana particle in a box, the nonzero components, and therefore the chiral wave functions, only admit the periodic and antiperiodic boundary conditions. From the latter two boundary conditions, we can only construct four boundary conditions for the entire Dirac wave function. Then, we demonstrate that these four boundary conditions are also included within the most general set of self-adjoint boundary conditions for a 1D Majorana particle in a box.
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