A coarse graining operation of spatially homogeneous quantum states based on an SU(1,1) Lie group structure has recently been proposed in (Bodendorfer and Haneder 2019 Phys. Lett. B 792 69–73) and used in (Bodendorfer and Wuhrer 2020 Class. Quantum Grav. 33 185007) to compute an explicit renormalisation group flow in the context of loop quantum cosmology. In this note, we explain the group theoretical origin of this procedure and generalise previous results based on these insights. We also highlight how the group theoretical origin of these techniques implies their immediate generalisation to other Lie groups.

最近在 (Bodendorfer and Haneder 2019 Phys. Lett. B 792 69-73) 中提出了基于 SU(1,1) 李群结构的空间均匀量子态的粗粒化操作，并在 (Bodendorfer and Wuhrer 2020 Class . Quantum Grav . 33 185007) 在环量子宇宙学的背景下计算显式重整化群流。在本说明中，我们解释了该程序的群体理论起源，并根据这些见解概括了先前的结果。我们还强调了这些技术的群理论起源如何暗示它们对其他李群的直接推广。