论文标题
超对称量子宇宙学中的形状不变电位
Shape Invariant Potentials in Supersymmetric Quantum Cosmology
论文作者
论文摘要
在这篇简短的评论中，我们评论了形状不变电位的概念，这是$ n = 2 $超对称量子力学的许多设置中的重要特征。为了激励其在超对称量子宇宙学中的应用，我们提出了一个案例研究，以说明这种有前途的工具的价值。具体而言，我们在一个单个标量场的存在下采用空间平坦的FRW模型，最小化与重力耦合。然后，我们提取关联的schrödinger-wheeler-dewitt方程，从而允许特定的因子排序范围。随后，我们计算相应的超对称合作伙伴汉密尔顿人，$ h_1 $和$ h_2 $。此外，我们指出了如何利用形状不变性属性来为我们的Schrödinger-Wheeler-Dewitt方程提供几个因素订购选择。取回基态，并容易写出激动的状态。最后，在$ n = 2 $超对称量子力学框架内明确显示了汉密尔顿人，$ h_1 $和$ h_2 $。
In this brief review, we comment on the concept of shape invariant potentials, which is an essential feature in many settings of $N=2$ supersymmetric quantum mechanics. To motivate its application within supersymmetric quantum cosmology, we present a case study to illustrate the value of this promising tool. Concretely, we take a spatially flat FRW model in the presence of a single scalar field, minimally coupled to gravity. Then, we extract the associated Schrödinger-Wheeler-DeWitt equation, allowing for a particular scope of factor ordering. Subsequently, we compute the corresponding supersymmetric partner Hamiltonians, $H_1$ and $H_2$. Moreover, we point out how the shape invariance property can be employed to bring a relation among several factor orderings choices for our Schrödinger-Wheeler-DeWitt equation. The ground state is retrieved, and the excited states easily written. Finally, the Hamiltonians, $H_1$ and $H_2$ are explicitly presented within a $N=2$ supersymmetric quantum mechanics framework.
