标题： 格点p形式电磁学与链场理论 显示英文标题

标题： Lattice p-Form Electromagnetism and Chain Field Theory

摘要： 自20世纪70年代威尔逊在格点规范理论方面的工作以来，场论的离散版本在基础物理中发挥了至关重要的作用。 但最近人们对某些规范理论的高维类似物产生了兴趣，例如p形式电磁理论，包括弦理论中的Kalb-Ramond场及其非阿贝尔推广。 人们希望以类似于格点规范理论的方式对这些“高阶规范理论”进行离散化，但需要在离散化中将基本几何结构的维度提升。 作为研究更一般的高阶规范理论离散版本的一步，我们考虑p形式电磁理论的情况。 我们证明，离散p形式电磁理论可以用交换群链复形的代数描述来简单表示。 此外，该模型允许具有相当一般几何结构的离散时空，这与通常与格点规范理论相关联的规则立方格点形成对比。 在构建了适用于p形式电磁理论的适当离散时空模型后，我们使用欧几里得路径积分形式主义对该理论进行量子化。 主要结果是将p形式电磁理论描述为一个“链场理论”——一种类似于拓扑量子场理论的理论，但用链复形代替流形。 特别是，这提供了一种从离散时空的一个“类空截面”到另一个“类空截面”的时间演化概念。 显示英文摘要

摘要： Since Wilson's work on lattice gauge theory in the 1970s, discrete versions of field theories have played a vital role in fundamental physics. But there is recent interest in certain higher dimensional analogues of gauge theory, such as p-form electromagnetism, including the Kalb-Ramond field in string theory, and its nonabelian generalizations. It is desirable to discretize such `higher gauge theories' in a way analogous to lattice gauge theory, but with the fundamental geometric structures in the discretization boosted in dimension. As a step toward studying discrete versions of more general higher gauge theories, we consider the case of p-form electromagnetism. We show that discrete p-form electromagnetism admits a simple algebraic description in terms of chain complexes of abelian groups. Moreover, the model allows discrete spacetimes with quite general geometry, in contrast to the regular cubical lattices usually associated with lattice gauge theory. After constructing a suitable model of discrete spacetime for p-form electromagnetism, we quantize the theory using the Euclidean path integral formalism. The main result is a description of p-form electromagnetism as a `chain field theory' -- a theory analogous to topological quantum field theory, but with chain complexes replacing manifolds. This, in particular, gives a notion of time evolution from one `spacelike slice' of discrete spacetime to another.