论文标题
$ \ Mathcal {n} = 1 $用LQG方法和SUSY约束的量化
$\mathcal{N}=1$ Supergravity with LQG methods and quantization of the SUSY constraint
论文作者
论文摘要
在本文中，将在环路量子重力的框架内研究$ \ Mathcal {n} = 1 $超级尺寸的经典和量子理论。我们讨论了Tsuda首次引入的超级实力霍斯特动作的规范分析。通过这种方式，我们还得出了超对称约束的紧凑表达，在规范的超级实力理论中起着至关重要的作用，类似于汉密尔顿约束在非苏皮比对称方面的共同协方差理论中的作用。然后，使用环路量子重力方法对所得理论进行量化。特别是，我们提出并讨论了超对称约束的量化，并得出了所得操作员作用的明确表达。这很重要，因为它是分析量子理论中超对称性和汉密尔顿约束产生的狄拉克代数的第一步。我们还讨论了SUSY约束解决方案的某些定性特性。
In this paper, the classical and quantum theory of $\mathcal{N}=1$ supergravity in four spacetime dimensions will be studied in the framework of loop quantum gravity. We discuss the canonical analysis of the supergravity Holst action as first introduced by Tsuda. In this way, we also derive a compact expression of the supersymmetry constraint, which plays a crucial role in canonical supergravity theories, akin to the role of the Hamiltonian constraint in non-supersymmetric generally covariant theories. The resulting theory is then quantized using loop quantum gravity methods. In particular, we propose and discuss a quantization of the supersymmetry constraint and derive explicit expressions of the action of the resulting operator. This is important as it is the first step on the way of analyzing the Dirac algebra generated by supersymmetry and Hamiltonian constraint in the quantum theory and for finding physical states. We also discuss some qualitative properties of such solutions of the SUSY constraint.
