二阶场论与高阶力学的阶数约化、可投影性及约束
数学物理
2017-12-29 v2 math.MP
摘要
在三阶射流丛 中，Poincaré-Cartan 形式向低阶射流丛的投影性（可投影性）是相应拉格朗日量退化特性的结果。利用 中伴随的欧拉-拉格朗日方程的约束算法分析了这一事实。该结果被应用于从多辛观点研究爱因斯坦方程（真空）的 Hilbert 拉格朗日量。因此我们展示了这些方程如何作为将约束算法应用于几何场方程的结果，同时其他约束与如下事实相关：该二阶理论等价于一个一阶理论。此外，高阶力学的情况也作为特例被研究。
引用
@article{arxiv.1604.02074,
title = {Order reduction, projectability and constraints of second-order field theories and higher-order mechanics},
author = {Jordi Gaset and Narciso Román-Roy},
journal= {arXiv preprint arXiv:1604.02074},
year = {2017}
}
备注
12 pages. Section 3 has been significantly enlarged (the Hilbert-Einstein Lagrangian is explained in more detail). The proofs of theorems 1 and 2 have been slightly enlarged to better explain the constraint algorithm. Some misprints have been corrected. The bibliography has been updated and some additional references are added. To be published in Reports on Mathematical Physics