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arXiv 2109.05596hep-th
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大质量场的前辛结构和内禀拉格朗日量

Presymplectic structures and intrinsic Lagrangians for massive fields

Maxim Grigoriev, Vyacheslav Gritzaenko

备注：
32 pages, v2: section on massive spin 3 added, comments and references added, a few typos fixed
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摘要：

我们研究的建设，所谓的内在行动的PDE配备兼容的前辛结构。特别地，我们明确地证明了标准爱因斯坦-希尔伯特引力的内禀作用量是熟悉的一阶Palatini作用量。在这项工作中，我们的主要重点是大规模的自旋2场，自然的前辛结构是不完整的，在这个意义上，相关的内在作用并没有重现所有的运动方程。我们明确地将这一功能的零阶微分后果在真正的拉格朗日制定的菲尔茨和泡利。此外，一个最小的多辛扩展的内在行动，产生所有的运动方程的构造和它认为，这种类型的系统可以自然地被视为多维类似物的机械系统的约束。最后，我们将考虑扩展到大质量自旋3场，并认为扩展到所有大质量更高的自旋也应该是简单的。

英文摘要：

We study the construction of the so-called intrinsic action for PDEs equipped with compatible presymplectic structures. In particular, we explicitly demonstrate that the intrinsic action for the standard Einstein-Hilbert gravity is the familiar first-order Palatini action. Our main focus in this work is the massive spin-2 field, where the natural presymplectic structure is not complete in the sense that the associated intrinsic action does not reproduce all the equations of motion. We explicitly relate this feature to the differential consequences of the zeroth order in the genuine Lagrangian formulation of Fierz and Pauli. Moreover, a minimal multisymplectic extension of the intrinsic action that produces all the equations of motion is constructed and it is argued that systems of this type can be naturally regarded as multidimensional analogs of mechanical systems with constraints. Finally, we extend the considerations to the massive spin-3 field and argue that the extension to all the massive higher spins should be straightforward as well.

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