In the fermionic systems with topologically stable Fermi points the emergent two-component Weyl fermions appear. We propose the topological classification of these fermions based on the two invariants composed of the two-component Green function. We define these invariants using Wigner–Weyl formalism also in case of essentially non-homogeneous systems. In the case when values of these invariants are minimal (±1) we deal with emergent relativistic symmetry. The emergent gravity appears, and our classification of Weyl fermions gives rise to the classification of vierbein. Transformations between emergent relativistic Weyl fermions of different types correspond to parity conjugation and charge conjugation.

在具有拓扑稳定的费米点的费米离子系统中，出现了出现的两组分韦尔费米子。我们基于由两个成分的格林函数组成的两个不变量，提出了这些费米子的拓扑分类。在基本非齐次系统的情况下，我们也使用Wigner-Weyl形式主义来定义这些不变量。在这些不变量的值最小（±1）的情况下，我们处理紧急相对论对称性。出现了引力，我们对Weyl费米子的分类引起了维尔贝因的分类。不同类型的出现的相对论性魏尔费米子之间的转换对应于奇偶共轭和电荷共轭。