We demonstrate explicitly the absence of the quantum corrections to the Carroll–Field–Jackiw (CFJ) term beyond one-loop within the Lorentz-breaking CPT-odd extension of QED. The proof holds within two prescriptions of quantum calculations, with the axial vector in the fermion sector treated either as a perturbation or as a contribution in the exact propagator of the fermion field.

中文翻译：

---

没有对 Carroll-Field-Jackiw 项的辐射修正超出单环阶数

我们明确地证明了在 QED 的洛伦兹破坏 CPT 奇数扩展中，除了单循环之外，没有对 Carroll-Field-Jackiw (CFJ) 项的量子校正。该证明适用于量子计算的两个规定，费米子扇区中的轴向矢量要么被视为微扰，要么被视为费米子场的精确传播子中的贡献。