Abstract Given a smooth family of massless free fermions parametrized by a base manifold B , we show that the (mathematically rigorous) Batalin–Vilkovisky quantization of the observables of this family gives rise to the determinant line bundle for the corresponding family of Dirac operators.

中文翻译：

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Batalin-Vilkovisky 形式主义和行列式线丛

摘要 给定一个由基本流形 B 参数化的平滑无质量自由费米子族，我们证明了这个族的可观测量的（数学上严格的）Batalin-Vilkovisky 量化产生了对应的狄拉克算子族的行列式线丛。