A note on coarse graining and group representations

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.

Automated summary

This paper discusses the coarse graining operation of spatially homogeneous quantum states based on an SU(1,1) Lie group structure and its application in loop quantum cosmology. It also generalizes previous results and implies immediate generalization to other Lie groups based on group theoretical insights.