Degenerate higher-order Maxwell theories in flat space-time
Abstract We consider, in Minkowski spacetime, higher-order Maxwell Lagrangians with terms quadratic in the derivatives of the field strength tensor, and study their degrees of freedom. Using a 3+1 decomposition of these Lagrangians, we extract the kinetic matrix for the components of the electric fi...
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| Format: | Article |
| Language: | English |
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2024-10-01
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| Series: | Journal of High Energy Physics |
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| Online Access: | https://doi.org/10.1007/JHEP10(2024)218 |
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| author | Aimeric Colléaux David Langlois Karim Noui |
| author_facet | Aimeric Colléaux David Langlois Karim Noui |
| author_sort | Aimeric Colléaux |
| collection | DOAJ |
| description | Abstract We consider, in Minkowski spacetime, higher-order Maxwell Lagrangians with terms quadratic in the derivatives of the field strength tensor, and study their degrees of freedom. Using a 3+1 decomposition of these Lagrangians, we extract the kinetic matrix for the components of the electric field, corresponding to second time derivatives of the gauge field. If the kinetic matrix is invertible, the theory admits five degrees of freedom, namely the usual two polarisations of a photon plus three extra degrees of freedom which are shown to be Ostrogradski ghosts. We also classify the cases where the kinetic matrix is non-invertible and, using analogous simple models, we argue that, even though the degeneracy conditions reduce the number of degrees of freedom, it does not seem possible to fully eliminate all potential Ostrogradski ghosts. |
| format | Article |
| id | doaj-art-f16c5da8b5344c47b6e1c7e22ddb2262 |
| institution | Kabale University |
| issn | 1029-8479 |
| language | English |
| publishDate | 2024-10-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj-art-f16c5da8b5344c47b6e1c7e22ddb22622024-12-08T12:12:25ZengSpringerOpenJournal of High Energy Physics1029-84792024-10-0120241012710.1007/JHEP10(2024)218Degenerate higher-order Maxwell theories in flat space-timeAimeric Colléaux0David Langlois1Karim Noui2Astrophysics Research Center, The Open University of IsraelAstrophysics Research Center, The Open University of IsraelAstrophysics Research Center, The Open University of IsraelAbstract We consider, in Minkowski spacetime, higher-order Maxwell Lagrangians with terms quadratic in the derivatives of the field strength tensor, and study their degrees of freedom. Using a 3+1 decomposition of these Lagrangians, we extract the kinetic matrix for the components of the electric field, corresponding to second time derivatives of the gauge field. If the kinetic matrix is invertible, the theory admits five degrees of freedom, namely the usual two polarisations of a photon plus three extra degrees of freedom which are shown to be Ostrogradski ghosts. We also classify the cases where the kinetic matrix is non-invertible and, using analogous simple models, we argue that, even though the degeneracy conditions reduce the number of degrees of freedom, it does not seem possible to fully eliminate all potential Ostrogradski ghosts.https://doi.org/10.1007/JHEP10(2024)218Effective Field TheoriesGauge SymmetryClassical Theories of Gravity |
| spellingShingle | Aimeric Colléaux David Langlois Karim Noui Degenerate higher-order Maxwell theories in flat space-time Journal of High Energy Physics Effective Field Theories Gauge Symmetry Classical Theories of Gravity |
| title | Degenerate higher-order Maxwell theories in flat space-time |
| title_full | Degenerate higher-order Maxwell theories in flat space-time |
| title_fullStr | Degenerate higher-order Maxwell theories in flat space-time |
| title_full_unstemmed | Degenerate higher-order Maxwell theories in flat space-time |
| title_short | Degenerate higher-order Maxwell theories in flat space-time |
| title_sort | degenerate higher order maxwell theories in flat space time |
| topic | Effective Field Theories Gauge Symmetry Classical Theories of Gravity |
| url | https://doi.org/10.1007/JHEP10(2024)218 |
| work_keys_str_mv | AT aimericcolleaux degeneratehigherordermaxwelltheoriesinflatspacetime AT davidlanglois degeneratehigherordermaxwelltheoriesinflatspacetime AT karimnoui degeneratehigherordermaxwelltheoriesinflatspacetime |