论文标题
标量电动力学作为3BF理论的哈密顿分析
Hamiltonian Analysis for the Scalar Electrodynamics as 3BF Theory
论文作者
论文摘要
可以通过从量规组的概念传递到量规3组的概念，将较高类别理论概括为所谓的3BF作用。耦合到爱因斯坦 - 卡丹重力的标量电动力学理论可以作为约束的3BF理论提出，用于特定选择量规3组。对与标量电动力学相对应的谎言3组的3BF作用进行了全面的汉密尔顿分析。该分析是朝着3BF理论进行规范量化的第一步，这是对完整标量电动力学量化的重要垫脚石，该量子与Einstein-Cartan重力耦合，该重力是由3BF动作配合的，具有适当的简单约束。结果表明，所产生的动态约束消除了所有传播自由度，即3组选择3组的理论是预期的拓扑字段理论。
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 3-group. The theory of scalar electrodynamics coupled to Einstein-Cartan gravity can be formulated as a constrained 3BF theory for a specific choice of the gauge 3-group. The complete Hamiltonian analysis of the 3BF action for the choice of a Lie 3-group corresponding to scalar electrodynamics is performed. This analysis is the first step towards a canonical quantization of a 3BF theory, an important stepping stone for the quantization of the complete scalar electrodynamics coupled to Einstein-Cartan gravity formulated as a 3BF action with suitable simplicity constraints. It is shown that the resulting dynamic constraints eliminate all propagating degrees of freedom, i.e., the 3BF theory for this choice of a 3-group is a topological field theory, as expected.
