Dualities of self-dual nonlinear electrodynamics
Abstract For any causal nonlinear electrodynamics theory that is “self-dual” (electromagnetic U(1)-duality invariant), the Legendre-dual pair of Lagrangian and Hamiltonian densities L H $$ \left\{\mathcal{L},\mathcal{H}\right\} $$ are constructed from functions ℓ h $$ \left\{\ell, \mathfrak{h}\right...
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2024-09-01
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| Series: | Journal of High Energy Physics |
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| Online Access: | https://doi.org/10.1007/JHEP09(2024)107 |
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| author | Jorge G. Russo Paul K. Townsend |
| author_facet | Jorge G. Russo Paul K. Townsend |
| author_sort | Jorge G. Russo |
| collection | DOAJ |
| description | Abstract For any causal nonlinear electrodynamics theory that is “self-dual” (electromagnetic U(1)-duality invariant), the Legendre-dual pair of Lagrangian and Hamiltonian densities L H $$ \left\{\mathcal{L},\mathcal{H}\right\} $$ are constructed from functions ℓ h $$ \left\{\ell, \mathfrak{h}\right\} $$ on ℝ + related to a particle-mechanics Lagrangian and Hamiltonian. We show how a ‘duality’ relating ℓ to h $$ \mathfrak{h} $$ implies that L $$ \mathcal{L} $$ and H $$ \mathcal{H} $$ are related by a simple map between appropriate pairs of variables. We also discuss Born’s “Legendre self-duality” and implications of a new “Φ-parity” duality. Our results are illustrated with many examples. |
| format | Article |
| id | doaj-art-859be989088241f48942e352235c7e45 |
| institution | Kabale University |
| issn | 1029-8479 |
| language | English |
| publishDate | 2024-09-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj-art-859be989088241f48942e352235c7e452024-12-08T12:16:42ZengSpringerOpenJournal of High Energy Physics1029-84792024-09-012024914110.1007/JHEP09(2024)107Dualities of self-dual nonlinear electrodynamicsJorge G. Russo0Paul K. Townsend1Institució Catalana de Recerca i Estudis Avançats (ICREA)Department of Applied Mathematics and Theoretical Physics, Centre for Mathematical Sciences, University of CambridgeAbstract For any causal nonlinear electrodynamics theory that is “self-dual” (electromagnetic U(1)-duality invariant), the Legendre-dual pair of Lagrangian and Hamiltonian densities L H $$ \left\{\mathcal{L},\mathcal{H}\right\} $$ are constructed from functions ℓ h $$ \left\{\ell, \mathfrak{h}\right\} $$ on ℝ + related to a particle-mechanics Lagrangian and Hamiltonian. We show how a ‘duality’ relating ℓ to h $$ \mathfrak{h} $$ implies that L $$ \mathcal{L} $$ and H $$ \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.https://doi.org/10.1007/JHEP09(2024)107Duality in Gauge Field TheoriesEffective Field Theories |
| spellingShingle | Jorge G. Russo Paul K. Townsend Dualities of self-dual nonlinear electrodynamics Journal of High Energy Physics Duality in Gauge Field Theories Effective Field Theories |
| title | Dualities of self-dual nonlinear electrodynamics |
| title_full | Dualities of self-dual nonlinear electrodynamics |
| title_fullStr | Dualities of self-dual nonlinear electrodynamics |
| title_full_unstemmed | Dualities of self-dual nonlinear electrodynamics |
| title_short | Dualities of self-dual nonlinear electrodynamics |
| title_sort | dualities of self dual nonlinear electrodynamics |
| topic | Duality in Gauge Field Theories Effective Field Theories |
| url | https://doi.org/10.1007/JHEP09(2024)107 |
| work_keys_str_mv | AT jorgegrusso dualitiesofselfdualnonlinearelectrodynamics AT paulktownsend dualitiesofselfdualnonlinearelectrodynamics |