论文标题
自dual循环量子宇宙学中的超对称迷你uperspace模型
Supersymmetric minisuperspace models in self-dual loop quantum cosmology
论文作者
论文摘要
在本文中，我们研究了使用自动偶数变量的$ \ Mathcal {n} = 1 $ SuperGravity的一类对称模型。它基于D'eath等人提出的Gravitino场的特定Ansatz。我们表明，经典理论中约束代数的基本部分是关闭的。特别是，左右超对称约束之间的（分级）泊松支架再现了汉密尔顿的约束。对于量子理论，我们将明显超对称方法的技术应用于循环量子超级重力，从而产生了圆形 - 频率代数和自然状态空间的分级类似物。我们在量子理论中实现其余约束。对于这些模型的某些子类，我们明确地表明，超对称约束的（分级）换向器完全重现了经典的泊松关系。特别是，左右超对称约束的换向器的痕迹再现了汉密尔顿约束操作员。最后，我们考虑了理论的动力学，并将其与标准变量和标准Minisuperspace技术进行比较。
In this paper, we study a class of symmetry reduced models of $\mathcal{N}=1$ supergravity using self-dual variables. It is based on a particular Ansatz for the gravitino field as proposed by D'Eath et al. We show that the essential part of the constraint algebra in the classical theory closes. In particular, the (graded) Poisson bracket between the left and right supersymmetry constraint reproduces the Hamiltonian constraint. For the quantum theory, we apply techniques from the manifestly supersymmetric approach to loop quantum supergravity, which yields a graded analog of the holonomy-flux algebra and a natural state space. We implement the remaining constraints in the quantum theory. For a certain subclass of these models, we show explicitly that the (graded) commutator of the supersymmetry constraints exactly reproduces the classical Poisson relations. In particular, the trace of the commutator of left and right supersymmetry constraints reproduces the Hamilton constraint operator. Finally, we consider the dynamics of the theory and compare it to a quantization using standard variables and standard minisuperspace techniques.
