Hamiltonian formulation of Carrollian Maxwell theory in deformed light-cone Kaluza-Klein-like null reduction

We construct magnetic and electric Carrollian Maxwell theories by performing Kaluza-Klein-like null reduction of a complex Maxwell field in a Bargmann deformed light-cone background with manifest gauge symmetry. The procedure preserves the original first-class U(1) Gauss constraint in the standard Carrollian Maxwell theories and deformed Carrollian Maxwell theories with a decoupled electric/magnetic scalar $A_-$. We emphasize that $A_-$ can be rendered non-dynamical by imposing additional ad hoc constraints. This corresponds to imposing the light-cone gauge $A_- = 0$ prior to the KK-like null reduction. For an electric pseudo-coupled theory without gauge symmetry, after imposing the ad hoc constraints the theory becomes the standard electric Maxwell theory together with a decoupled zero-energy scalar $A_-$. Furthermore, our work provides an explicit example of the correct application of this approach, thereby broadening the scope of its applicability to gauge theories.