论文标题
Premplectic Gauge PDE和Lagrangian BV形式主义超越喷气式
Presymplectic gauge PDEs and Lagrangian BV formalism beyond jet-bundles
论文作者
论文摘要
量规PDE是物理学家所谓的局部量规理论的几何对象，该理论在运动方程级别定义了（即不指定拉格朗日），以Batalin-vilkovisky（BV）形式主义。这一概念一方面用喷射束和对PDE的几何方法扩展了BV公式。在这项工作中，我们集中于配备兼容的预透明结构的量规PDE，并表明在某些规律性条件下，该数据定义了喷气型BV公式。更确切地说，BV喷射束作为初始量规PDE的超级喷射束的符号商商而出现。从这个意义上讲，Per-eplectial Gauge PDE为Lagrangian仪表系统提供了不变的几何方法，该方法不限于喷气束。此外，预成立量规PDE结构自然降落到时空submanifolds（尤其是边界（如果有的话）），并且在这方面，与已知具有此特征的Aksz Sigma模型非常相似。我们还引入了一个弱的前量规PDE的概念，其中差异的固定性被BV主方程的前胶质类似物代替，并表明它仍然定义了局部BV系统。这允许一个人用有限的分级几何形状编码BV系统，就像AKSZ结构在拓扑模型的情况下一样。
A gauge PDE is a geometrical object underlying what physicists call a local gauge field theory defined at the level of equations of motion (i.e. without specifying Lagrangian) in terms of Batalin-Vilkovisky (BV) formalism. This notion extends the BV formulation in terms of jet-bundles on the one hand and the geometrical approach to PDEs on the other hand. In this work we concentrate on gauge PDEs equipped with a compatible presymplectic structure and show that under some regularity conditions this data defines a jet-bundle BV formulation. More precisely, the BV jet-bundle arises as the symplectic quotient of the super jet-bundle of the initial gauge PDE. In this sense, presymplectic gauge PDEs give an invariant geometrical approach to Lagrangian gauge systems, which is not limited to jet-bundles. Furthermore, the presymplectic gauge PDE structure naturally descends to space-time submanifolds (in particular, boundaries, if any) and, in this respect, is quite similar to AKSZ sigma models which are long known to have this feature. We also introduce a notion of a weak presymplectic gauge PDE, where the nilpotency of the differential is replaced by a presymplectic analog of the BV master equation, and show that it still defines a local BV system. This allows one to encode BV systems in terms of finite-dimensional graded geometry, much like the AKSZ construction does in the case of topological models.
