Abstract
Based on the method of computing the curl of vector, axial-vector and the tensor current operator equations, the possible quantum anomaly for the transverse Ward–Takahashi relations in QED3 and QED2 theories is studied. The absence of transverse anomalies for both axial-vector current in QED2 theory and vector (tensor) current in QED3 theory are verified respectively. Further, it is found that when we ignore the contribution of the three integral-term involving the vertex function in the Wilson line, we can get a set of closed coupled integral Dyson–Schwinger equations in QED3.
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