Clarify the split between Carrollian momenta and hypermomenta

Establish a systematic understanding of the split between Carrollian momenta and hypermomenta, and consequently between charge and flux, in Carrollian theories with independent connection data.

Background

In the proposed Carrollian formulation, the momenta encode charge-aspect information while the hypermomenta encode responses to the independent radiative connection sector. Because part of the connection is related to frame geometry and part is independent, the division between momentum and hypermomentum—and therefore between charge and flux—is not unique.

The paper explains that this ambiguity affects whether the resulting Ward identities appear as ordinary conservation laws or as evolution equations with curvature-flux terms. It explicitly identifies a systematic account of this distinction as an open problem.