Hamiltonian formulation of Carrollian Maxwell theory in Deformed Light-cone Kaluza-Klein-like Null reduction
Abstract
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 give the scaling of the parent gauge parameter and show that the U(1) symmetry is inherited from the parent theory and not introduced after the limit. We emphasize that A- can be rendered non-dynamical by imposing additional ad hoc constraints. Since A- is invariant under the original U(1) symmetry, removing it is a constraint and not a gauge choice, but the resulting theory is the same as the one reached by 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.
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BibTeX
@misc{zeng2026hamiltonian,
title = {{Hamiltonian formulation of Carrollian Maxwell theory in Deformed Light-cone Kaluza-Klein-like Null reduction}},
author = {Limin Zeng},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2606.22050},
eprint = {2606.22050},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2606.22050},
}
RIS
TY - UNPB
TI - Hamiltonian formulation of Carrollian Maxwell theory in Deformed Light-cone Kaluza-Klein-like Null reduction
AU - Limin Zeng
PY - 2026
DA - 2026/10/22
PB - arXiv
DO - 10.48550/arxiv.2606.22050
UR - https://arxiv.org/abs/2606.22050
AB - 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 give the scaling of the parent gauge parameter and show that the U(1) symmetry is inherited from the parent theory and not introduced after the limit. We emphasize that A_- can be rendered non-dynamical by imposing additional ad hoc constraints. Since A_- is invariant under the original U(1) symmetry, removing it is a constraint and not a gauge choice, but the resulting theory is the same as the one reached by 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.
ER -