论文标题
邀请主要系列
An invitation to the principal series
论文作者
论文摘要
等轴测组的标量统一表示$ d $ d $ d $二维的固定空间$ so（1，d）$由它们的保形权重$δ$标记。 De Sitter空间的一个显着特征是，与Sitter Scale相比，具有足够大质量的标量字段$ 1/\ Ell $具有复杂的保形权重，并且这些字段的物理模式属于$ SO（1，d）$的单一连续主序列表示。我们的目标是在$ d = 2 $中研究这些表示形式，其中相关组为$ sl（2，\ mathbb {r}）$。我们表明，作用在大规模标量场上的DS $ _2 $的等轴测组的发电机再现了De Alfaro，Fubini和Furlan（DFF）引入的量子机械模型，并在早期/晚期限制中。由环境DS $ _2 $构造的动机，我们详细介绍了如何更改DFF模型以适应主要系列表示形式。我们指出了为该模型写下经典的拉格朗日语的困难，而规范的汉密尔顿公式则避免了任何问题。我们从该玩具模型的角度推测了各种保姆不变真空吸尘器的含义，并讨论了一些潜在的概括。
Scalar unitary representations of the isometry group of $d$-dimensional de Sitter space $SO(1,d)$ are labeled by their conformal weights $Δ$. A salient feature of de Sitter space is that scalar fields with sufficiently large mass compared to the de Sitter scale $1/\ell$ have complex conformal weights, and physical modes of these fields fall into the unitary continuous principal series representation of $SO(1,d)$. Our goal is to study these representations in $d=2$, where the relevant group is $SL(2,\mathbb{R})$. We show that the generators of the isometry group of dS$_2$ acting on a massive scalar field reproduce the quantum mechanical model introduced by de Alfaro, Fubini and Furlan (DFF) in the early/late time limit. Motivated by the ambient dS$_2$ construction, we review in detail how the DFF model must be altered in order to accommodate the principal series representation. We point out a difficulty in writing down a classical Lagrangian for this model, whereas the canonical Hamiltonian formulation avoids any problem. We speculate on the meaning of the various de Sitter invariant vacua from the point of view of this toy model and discuss some potential generalizations.
