AI 中文总结
该研究在pAQFT框架内将规范场论量子化，纳入局部函子方法关键方面，给出修正主方程表述及构建重整化量子BFV算子方法；发现考虑边界时相关李代数弯曲，恢复了一些先前结果。
AI 中文摘要
我们在由巴塔林、弗拉德金、维尔科夫斯基形式体系（BV/BFV）丰富的微扰代数量子场论（pAQFT）框架内，对具有标记超曲面的全局双曲洛伦兹流形上的规范场论进行量子化。这使得在代数框架中纳入具有边界的流形上规范场论的局部函子方法的一些关键方面。特别地，我们给出了修正的经典和量子主方程（仿照卡塔内奥、姆涅夫和雷谢蒂金CMR）的pAQFT表述，以及通过边界项构建重整化量子BFV算子以修正量子主方程失效的构造方法。我们发现，当考虑边界时，由反常主沃德恒等式产生的重整化量子同伦dg李代数会弯曲。量子主方程的失效因此由一个非平凡曲率项编码在一个$L_\infty$代数中。作为副产品，我们恢复了霍兰兹关于（边界）BRST荷与BV算子关系的先前结果，以及CMR在阿贝尔杨 - 米尔斯理论中因果柱体上领先微扰阶的量子BFV算子的假设。
英文摘要
We formulate quantisation of gauge field theories on globally hyperbolic Lorentzian manifolds with marked hypersurfaces within the framework of perturbative algebraic quantum field theory (pAQFT) enriched by the Batalin, Fradkin, Vilkovisky formalism (BV/BFV). This allows one to incorporate some crucial aspects of the local functorial approach to gauge field theory on manifolds with boundary within the algebraic setting. In particular, we provide a pAQFT-formulation of the modified classical and quantum master equations (after Cattaneo, Mnev and Reshetikhin CMR), as well as a constructive way to build a renormalised quantum BFV operator correcting the failure of the Quantum Master Equation by means of boundary terms (in the appropriate sense). We find that the renormalised quantum homotopy dg Lie algebra arising from the Anomalous Master Ward Identity becomes curved when boundaries are considered. The failure of the quantum master equation is thus encoded by a nontrivial curvature term in an $L_\infty$ algebra. As a byproduct, we recover previous results of Hollands' on the relation between the (boundary) BRST charge and the BV operator, and we recover CMR's ansatz for the quantum BFV operator at leading perturbative order on causal cylinders in Abelian Yang--Mills theory.
Comments62pp + refs
