Higher-order and non-geometric symmetries and Noether's theorem in k-cosymplectic Hamiltonian field theory
Abstract
In this paper, we investigate higher-order symmetries and non-geometric symmetries within the framework of k-cosymplectic Hamiltonian field theory. We introduce the concept of generalized infinitesimal symmetry, which relaxes the standard symmetry condition, and then define two new classes of symmetries: higher-order general infinitesimal Cartan symmetries and good non-geometric symmetries. For each of these symmetry classes, we establish a Noether-type theorem that provides explicit conserved quantities for exact k-cosymplectic Hamiltonian systems. These results extend and generalize previous work on standard Cartan symmetries in the k-cosymplectic setting. Furthermore, we extend all of these results in a parallel fashion to Hamiltonian systems on k-symplectic manifolds, demonstrating the unifying nature of our approach. Concrete examples are provided to illustrate the existence and applicability of the proposed symmetries. Our framework offers a systematic geometric treatment of generalized symmetries and their associated conservation laws in classical field theories.
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BibTeX
@misc{leon2026higherorder,
title = {{Higher-order and non-geometric symmetries and Noether's theorem in k-cosymplectic Hamiltonian field theory}},
author = {Manuel de León and Xuefeng Zhao},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.23034},
eprint = {2609.23034},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.23034},
}
RIS
TY - UNPB
TI - Higher-order and non-geometric symmetries and Noether's theorem in k-cosymplectic Hamiltonian field theory
AU - Manuel de León
AU - Xuefeng Zhao
PY - 2026
DA - 2026/09/19
PB - arXiv
DO - 10.48550/arxiv.2609.23034
UR - https://arxiv.org/abs/2609.23034
AB - In this paper, we investigate higher-order symmetries and non-geometric symmetries within the framework of k-cosymplectic Hamiltonian field theory. We introduce the concept of generalized infinitesimal symmetry, which relaxes the standard symmetry condition, and then define two new classes of symmetries: higher-order general infinitesimal Cartan symmetries and good non-geometric symmetries. For each of these symmetry classes, we establish a Noether-type theorem that provides explicit conserved quantities for exact k-cosymplectic Hamiltonian systems. These results extend and generalize previous work on standard Cartan symmetries in the k-cosymplectic setting. Furthermore, we extend all of these results in a parallel fashion to Hamiltonian systems on k-symplectic manifolds, demonstrating the unifying nature of our approach. Concrete examples are provided to illustrate the existence and applicability of the proposed symmetries. Our framework offers a systematic geometric treatment of generalized symmetries and their associated conservation laws in classical field theories.
ER -