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| Format: | Preprint |
| Veröffentlicht: |
2024
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| Schlagworte: | |
| Online-Zugang: | https://arxiv.org/abs/2407.02577 |
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| _version_ | 1866909317148442624 |
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| author | Russo, Jorge G. Townsend, Paul K. |
| author_facet | Russo, Jorge G. Townsend, Paul K. |
| contents | For any causal nonlinear electrodynamics theory that is "self-dual" (electromagnetic $U(1)$-duality invariant), the Legendre-dual pair of Lagrangian and Hamiltonian densities $\{\mathcal{L},\mathcal{H}\}$ are constructed from functions $\{\ell,h\}$ on ${\bf R}^+$ related to a particle-mechanics Lagrangian and Hamiltonian. We show how a `duality' relating $\ell$ to $h$ implies that $\mathcal{L}$ and $\mathcal{H}$ are related by a simple map between appropriate pairs of variables. We also discuss Born's "Legendre self-duality" and implications of a new "$Φ$-parity" duality. Our results are illustrated with many examples. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_02577 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Dualities of Self-Dual Nonlinear Electrodynamics Russo, Jorge G. Townsend, Paul K. High Energy Physics - Theory For any causal nonlinear electrodynamics theory that is "self-dual" (electromagnetic $U(1)$-duality invariant), the Legendre-dual pair of Lagrangian and Hamiltonian densities $\{\mathcal{L},\mathcal{H}\}$ are constructed from functions $\{\ell,h\}$ on ${\bf R}^+$ related to a particle-mechanics Lagrangian and Hamiltonian. We show how a `duality' relating $\ell$ to $h$ implies that $\mathcal{L}$ and $\mathcal{H}$ are related by a simple map between appropriate pairs of variables. We also discuss Born's "Legendre self-duality" and implications of a new "$Φ$-parity" duality. Our results are illustrated with many examples. |
| title | Dualities of Self-Dual Nonlinear Electrodynamics |
| topic | High Energy Physics - Theory |
| url | https://arxiv.org/abs/2407.02577 |