In this paper, we find apart from the Ward–Takahashi (WT) identity, the identity between gamma matrices can also constrain the vertex functions in low-dimensional gauge theories. In (1 + 1) dimensions, the identity between gamma matrices gives the identity between vector and axial-vector vertex functions while in (2 + 1) dimensions it leads to the identity between vector and tensor vertex functions. Then, we derive the expressions of the full scalar, vector and tensor vertex functions in (2 + 1) dimensions Quantum Electrodynamics (QED3) by using the longitudinal and transverse WT identities for vector and tensor currents. Furthermore, we find that in the chiral limit with zero fermion masses, the contribution of Wilson line in full vector vertex function is eliminated and the full vector vertex function is strictly expressed in terms of the fermion propagators when using the identity between vector and tensor vertex functions to further constraint the vertex functions.

中文翻译：

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无质量 QED3 理论中受纵向和横向 Ward-Takahashi 恒等式约束的完整顶点函数

在本文中，我们发现除了 Ward-Takahashi (WT) 恒等式外，伽马矩阵之间的恒等式还可以约束低维规范理论中的顶点函数。在 (1 + 1) 维中，伽马矩阵之间的恒等式给出向量和轴向向量顶点函数之间的恒等，而在 (2 + 1) 维中，它导致向量和张量顶点函数之间的恒等式。然后，我们推导出 (2 + 1) 维量子电动力学 (QED) 中全标量、向量和张量顶点函数的表达式3) 通过使用矢量和张量电流的纵向和横向 WT 恒等式。此外，我们发现在零费米子质量的手征极限中，威尔逊线在全向量顶点函数中的贡献被消除了，当使用向量和张量顶点之间的恒等式时，全向量顶点函数严格地表示为费米子传播子。函数进一步约束顶点函数。