On auxiliary fields and Lagrangians for relativistic wave equations
| Autor: | Sharapov, Alexey, Shcherbatov, David |
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| Rok vydání: | 2023 |
| Předmět: | |
| Zdroj: | J. Phys. A: Math. Theor. 57 (2024) 015210 (22pp) |
| Druh dokumentu: | Working Paper |
| Popis: | We address the problem of the existence of a Lagrangian for a given system of linear PDEs with constant coefficients. As a subtask, this involves bringing the system into a pre-Lagrangian form, wherein the number of equations matches the number of unknowns. We introduce a class of overdetermined systems, called co-flat, and show that they always admit a pre-Lagrangian form, which can be explicitly constructed using auxiliary variables. Moreover, we argue that such systems enjoy pre-Lagrangian formulations without auxiliary variables at all. As an application of our method, we construct new pre-Lagrangian and Lagrangian formulations for free massive fields of arbitrary integer spin. In contrast to the well-known models of Singh and Hagen, our Lagrangians involve much fewer auxiliary fields. Comment: 17 pages; v2 - minor corrections, references added; v3 - journal version |
| Databáze: | arXiv |
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