Derive charge constancy from the kinematic framework

Establish, from principles internal to the kinematic classification of twisted cotangent-bundle symplectic structures, a principle that rules out position-dependent multipliers and thereby derives the constancy of the charge of a single particle.

Background

The kinematic classification permits a multiplier of the closed two-form defining the symplectic twist to vary with position in low-rank cases, including on a surface where the closure condition imposes no restriction on the multiplier. The manuscript imposes constancy only through an external invariance requirement and the interpretation of the multiplier as the charge of one particle.

The authors explicitly identify the absence of an internally derived constancy principle as an unresolved issue. Resolving it would make the treatment of charge more intrinsic to the construction rather than dependent on an additional constitutive declaration.

References

Let us set out the matters we leave open. The first is the multiplier, with which our own method is least at ease. The rank analysis of Section~\ref{sec.charge} settles what the classification asks of the charge, which above rank four is constancy and on a surface is nothing at all. A charge varying from place to place is therefore left standing by the geometry. What excludes it comes from outside, in the invariance requirement we import and in our own reading of the multiplier as the charge of one particle. A manuscript which admits each structure at the point of need, and marks each declaration where it is made, would rather have derived that one. Settling it from within would take a principle of invariance for inertial motion stronger than the one we have, and we do not have it.

— The kinematic structures and the inertial geometry of a moving charge  (2609.11165 - López-Monsalvo, 10 Sep 2026) in Section 6, Final remarks