Strict representative of the external translation class

Determine whether the external translation class of the independent-connection Weyl gauge theory admits a strictly invariant representative, beyond the metric theorem cited for the corresponding metric theory.

Background

The paper distinguishes internal translations introduced as a Stueckelberg redundancy from external translations, whose localization produces spacetime transformations. The internal construction yields an invariant coframe source, but the authors emphasize that this does not settle the existence of a strictly invariant local representative for the external translation Noether class of the full independent-connection theory.

The unresolved issue is whether the no-go result established for certain metric theories extends to the independent-connection Weyl gauge theory considered here. The paper explicitly leaves this question unsettled rather than proving either existence or nonexistence.

References

Whether the external translation class of this independent-connection theory admits a strictly invariant representative is not settled by the metric theorem of Ref. and remains open here.

— Internal translation gauging and local gravitational energy in Weyl gauge theory  (2610.13777 - Hobson et al., 9 Oct 2026) in Section 2, subsection “The status of the simplifying conditions”