The higher category theory can be employed to generalize the BF action to the so-called 3BF action, by passing from the notion of a gauge group to the notion of a gauge three-group. In this work we determine the full gauge symmetry of the 3BF action. To that end, the complete Hamiltonian analysis of the 3BF action for an arbitrary semistrict Lie three-group is performed, by using the Dirac procedure. The Hamiltonian analysis is the first step towards a canonical quantization of a 3BF theory. This is an important stepping-stone for the quantization of the complete standard model of elementary particles coupled to Einstein–Cartan gravity, formulated as a 3BF action with suitable simplicity constraints. We show that the resulting gauge symmetry group consists of the familiar G-, H-, and L-gauge transformations, as well as additional M- and N-gauge transformations, which have not been discussed in the existing literature.

中文翻译：

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一般半严格李三群的 3BF 理论的规范对称性

可以使用更高范畴理论来概括高炉对所谓的3采取行动高炉行动，通过从规范群的概念转移到规范三群的概念。在这项工作中，我们确定了 3 的全规范对称性高炉行动。为此，对 3 的完整哈密顿分析高炉通过使用 Dirac 程序执行任意半严格李三群的操作。哈密​​顿分析是迈向 a 3 规范量化的第一步高炉理论。这是量化与爱因斯坦-嘉当引力耦合的基本粒子的完整标准模型的重要垫脚石，公式为 3高炉具有适当简单约束的动作。我们表明，由此产生的规范对称群由熟悉的G-,H-， 和大号-gauge 转换，以及额外的米- 和否-规范转换，这在现有文献中尚未讨论。