Effective Field Theories as Lagrange Spaces
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866913228294979584 |
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| author | Craig, Nathaniel Lee, Yu-Tse Lu, Xiaochuan Sutherland, Dave |
| author_facet | Craig, Nathaniel Lee, Yu-Tse Lu, Xiaochuan Sutherland, Dave |
| contents | We present a formulation of scalar effective field theories in terms of the geometry of Lagrange spaces. The horizontal geometry of the Lagrange space generalizes the Riemannian geometry on the scalar field manifold, inducing a broad class of affine connections that can be used to covariantly express and simplify tree-level scattering amplitudes. Meanwhile, the vertical geometry of the Lagrange space characterizes the physical validity of the effective field theory, as a torsion component comprises strictly higher-point Wilson coefficients. Imposing analyticity, unitarity, and symmetry on the theory then constrains the signs and sizes of derivatives of the torsion component, implying that physical theories correspond to a special class of vertical geometry. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2305_09722 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Effective Field Theories as Lagrange Spaces Craig, Nathaniel Lee, Yu-Tse Lu, Xiaochuan Sutherland, Dave High Energy Physics - Theory High Energy Physics - Phenomenology We present a formulation of scalar effective field theories in terms of the geometry of Lagrange spaces. The horizontal geometry of the Lagrange space generalizes the Riemannian geometry on the scalar field manifold, inducing a broad class of affine connections that can be used to covariantly express and simplify tree-level scattering amplitudes. Meanwhile, the vertical geometry of the Lagrange space characterizes the physical validity of the effective field theory, as a torsion component comprises strictly higher-point Wilson coefficients. Imposing analyticity, unitarity, and symmetry on the theory then constrains the signs and sizes of derivatives of the torsion component, implying that physical theories correspond to a special class of vertical geometry. |
| title | Effective Field Theories as Lagrange Spaces |
| topic | High Energy Physics - Theory High Energy Physics - Phenomenology |
| url | https://arxiv.org/abs/2305.09722 |