Hamiltonian Analysis for the Scalar Electrodynamics as 3BF Theory
Hamiltonian Analysis for the Scalar Electrodynamics as 3BF Theory
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DOI：
10.3390/sym12040620
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发表时间：
2020-04
期刊：
影响因子：
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通讯作者：
T. Radenković;M. Vojinović
中科院分区：
文献类型：
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作者：
T. Radenković;M. Vojinović
通过从规范群的概念过渡到规范3-群的概念，可以利用高范畴理论将B F作用推广到所谓的3 B F作用。标量电动力学与爱因斯坦-嘉当引力耦合的理论可以表述为一个约束3 B F理论，用于规范3-群的特定选择。对3 B F作用量进行了完全的哈密顿分析，并选择了对应于标量电动力学的李3群.这种分析是迈向正则量子化的3 B F理论的第一步，这是耦合到爱因斯坦-嘉当引力的完全标量电动力学的量子化的重要垫脚石，其被制定为具有适当的简单性约束的3 B F作用。结果表明，由此产生的动态约束消除了所有的传播自由度，即，正如所预期，选择3-群的3 B F理论是拓扑场论。
The higher category theory can be employed to generalize the B F action to the so-called 3 B F 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 3 B F theory for a specific choice of the gauge 3-group. The complete Hamiltonian analysis of the 3 B F 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 3 B F theory, an important stepping stone for the quantization of the complete scalar electrodynamics coupled to Einstein–Cartan gravity formulated as a 3 B F action with suitable simplicity constraints. It is shown that the resulting dynamic constraints eliminate all propagating degrees of freedom, i.e., the 3 B F theory for this choice of a 3-group is a topological field theory, as expected.