利用超对称性推导指标定理
Derivation of Index theorem by Supersymmetry
摘要：
本文利用超对称$σ$模型，给出了Atiyah-Singer定理的几种特殊情形的详细计算.在计算路径积分的涨落算子的行列式时，采用了一些技巧。采用直观的几何论证克服了自旋场被规范场扭曲的复杂计算。
英文摘要：
The present paper gives calculations in detail to prove several special cases of Atiyah-Singer theorem through supersymmetric $σ$-models. Some technical tricks are employed to calculate the determinants of fluctuation operators of the path integrals. An intuitive and geometric argument is applied to overcome the complicated calculation on spin fields twisted by gauge fields.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
