标题： 局部规范理论的预辛极小模型 显示英文标题

标题： Presymplectic minimal models of local gauge theories

摘要： 我们详细阐述了最近提出的弱预辛规范PDE的概念。 它是在时空流形上的$\mathbb{Z}$-分次丛，配备了一个次数为$1$的向量场和一个相容的分次预辛结构。 这种几何数据自然定义了一个拉格朗日规范场论。 此外，它不仅编码了该理论的拉格朗日量，还编码了其完整的巴塔林-维列罗斯基（BV）形式化。 特别是，相应的场-反场空间作为初始纤维丛的超喷射丛的辛商出现。 这种方法的一个显著特点是，在编码给定规范理论的各种预辛规范PDE中，我们可以选择一个最小的，通常为有限维的，并在某种意义上是唯一的。 这种方法可以看作是熟悉的AKSZ构造对不一定拓扑且不具有微分同胚不变性的理论的扩展。 我们给出了多种例子，包括$p$-形式、手征杨-米尔斯理论、霍尔斯特引力和共形引力。 我们还解释了与该形式化非BV-BRST版本的显式关系，这恰好与协变相空间和多重辛方法密切相关。 显示英文摘要

摘要： We elaborate on the recently proposed notion of a weak presymplectic gauge PDE. It is a $\mathbb{Z}$-graded bundle over the space-time manifold, equipped with a degree $1$ vector field and a compatible graded presymplectic structure. This geometrical data naturally defines a Lagrangian gauge field theory. Moreover, it encodes not only the Lagrangian of the theory but also its full-scale Batalin-Vilkovisky (BV) formulation. In particular, the respective field-antifield space arises as a symplectic quotient of the super-jet bundle of the initial fiber bundle. A remarkable property of this approach is that among the variety of presymplectic gauge PDEs encoding a given gauge theory we can pick a minimal one that usually turns out to be finite-dimensional, and unique in a certain sense. The approach can be considered as an extension of the familiar AKSZ construction to not necessarily topological and diffeomorphism-invariant theories. We present a variety of examples including $p$-forms, chiral Yang-Mills theory, Holst gravity, and conformal gravity. We also explain the explicit relation to the non-BV-BRST version of the formalism, which happens to be closely related to the covariant phase space and the multisymplectic approaches.