Higher spins and Finsler geometry
Abstract Finsler geometry is a natural generalization of (pseudo-)Riemannian geometry, where the line element is not the square root of a quadratic form but a more general homogeneous function. Parameterizing this in terms of symmetric tensors suggests a possible interpretation in terms of higher-sp...
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| Format: | Article |
| Language: | English |
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SpringerOpen
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)047 |
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| author | Alessandro Tomasiello |
| author_facet | Alessandro Tomasiello |
| author_sort | Alessandro Tomasiello |
| collection | DOAJ |
| description | Abstract Finsler geometry is a natural generalization of (pseudo-)Riemannian geometry, where the line element is not the square root of a quadratic form but a more general homogeneous function. Parameterizing this in terms of symmetric tensors suggests a possible interpretation in terms of higher-spin fields. We will see here that, at linear level in these fields, the Finsler version of the Ricci tensor leads to the curved-space Fronsdal equation for all spins, plus a Stueckelberg-like coupling. Nonlinear terms can also be systematically analyzed, suggesting a possible interacting structure. No particular choice of spacetime dimension is needed. The Stueckelberg mechanism breaks gauge transformations to a redundancy that does not change the geometry. This creates a serious issue: non-transverse modes are not eliminated, at least for the versions of Finsler dynamics examined in this paper. |
| format | Article |
| id | doaj-art-a529f6411c9b4bfbbc0b9ac94e344dd7 |
| 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-a529f6411c9b4bfbbc0b9ac94e344dd72024-12-08T12:10:32ZengSpringerOpenJournal of High Energy Physics1029-84792024-10-0120241013210.1007/JHEP10(2024)047Higher spins and Finsler geometryAlessandro Tomasiello0Dipartimento di Matematica, Università degli Studi di Milano-BicoccaAbstract Finsler geometry is a natural generalization of (pseudo-)Riemannian geometry, where the line element is not the square root of a quadratic form but a more general homogeneous function. Parameterizing this in terms of symmetric tensors suggests a possible interpretation in terms of higher-spin fields. We will see here that, at linear level in these fields, the Finsler version of the Ricci tensor leads to the curved-space Fronsdal equation for all spins, plus a Stueckelberg-like coupling. Nonlinear terms can also be systematically analyzed, suggesting a possible interacting structure. No particular choice of spacetime dimension is needed. The Stueckelberg mechanism breaks gauge transformations to a redundancy that does not change the geometry. This creates a serious issue: non-transverse modes are not eliminated, at least for the versions of Finsler dynamics examined in this paper.https://doi.org/10.1007/JHEP10(2024)047Classical Theories of GravityDifferential and Algebraic GeometryHigher Spin GravityHigher Spin Symmetry |
| spellingShingle | Alessandro Tomasiello Higher spins and Finsler geometry Journal of High Energy Physics Classical Theories of Gravity Differential and Algebraic Geometry Higher Spin Gravity Higher Spin Symmetry |
| title | Higher spins and Finsler geometry |
| title_full | Higher spins and Finsler geometry |
| title_fullStr | Higher spins and Finsler geometry |
| title_full_unstemmed | Higher spins and Finsler geometry |
| title_short | Higher spins and Finsler geometry |
| title_sort | higher spins and finsler geometry |
| topic | Classical Theories of Gravity Differential and Algebraic Geometry Higher Spin Gravity Higher Spin Symmetry |
| url | https://doi.org/10.1007/JHEP10(2024)047 |
| work_keys_str_mv | AT alessandrotomasiello higherspinsandfinslergeometry |