Determine whether charge quantization reflects a broader rule

Determine whether the restriction of admissible charge values imposed by prequantization in the presence of a nonzero monopole flux is specific to electromagnetism or is an instance of a wider principle governing particle-dependent constitutive quantities.

Background

For the Dirac monopole on the round sphere, requiring the twisted symplectic form to admit a prequantum line bundle restricts the charge to the lattice q in (hbar/(2k)) times the integers. The quantization arises because the charge multiplies the cohomology class of the magnetic field.

The authors explicitly raise, but do not resolve, whether this partial closure of a constitutive freedom by geometry and prequantization is peculiar to electromagnetism or represents a general rule applicable to other particle-dependent quantities or theories.

References

The mass and the spin have been treated in this manner before. The charge is the third. Each is a freedom which inertial motion leaves open and which a particle closes on its own account. The charge is the one of the three which the geometry closes in part as well, once a prequantum bundle is needed. Whether that belongs to electromagnetism alone, or is the first instance of a wider rule, we raise here without settling.

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