Conservation laws in Lie-Poisson classical field theories
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866908952877334528 |
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| author | Abla, O. Neves, M. J. |
| author_facet | Abla, O. Neves, M. J. |
| contents | Lie-Poisson classical field theory is a field-theoretical model embedded in a non-commutative structure related to the framework of Poisson electrodynamics. In this paper, we follow the recently developed action principle for Lie-Poisson electrodynamics to derive the conservation laws of the theory. The energy-momentum tensor is obtained, along with the conserved electric charge and the momentum operator. We consider non-interacting examples for real and complex scalar fields, as well as the Dirac field, within the $κ$-Minkowski spacetime framework. In the latter case, we show that the non-relativistic limit for the $κ$-Minkowski Dirac equation introduces an orbital Zeeman coupling term for the fermionic fields, and the energy shift in the first excited state depends exclusively on the $κ$-parameter. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_09500 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Conservation laws in Lie-Poisson classical field theories Abla, O. Neves, M. J. High Energy Physics - Theory Lie-Poisson classical field theory is a field-theoretical model embedded in a non-commutative structure related to the framework of Poisson electrodynamics. In this paper, we follow the recently developed action principle for Lie-Poisson electrodynamics to derive the conservation laws of the theory. The energy-momentum tensor is obtained, along with the conserved electric charge and the momentum operator. We consider non-interacting examples for real and complex scalar fields, as well as the Dirac field, within the $κ$-Minkowski spacetime framework. In the latter case, we show that the non-relativistic limit for the $κ$-Minkowski Dirac equation introduces an orbital Zeeman coupling term for the fermionic fields, and the energy shift in the first excited state depends exclusively on the $κ$-parameter. |
| title | Conservation laws in Lie-Poisson classical field theories |
| topic | High Energy Physics - Theory |
| url | https://arxiv.org/abs/2604.09500 |