作用相关爱因斯坦-希尔伯特拉格朗日场方程的变分推导

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2022-06-23 DOI:10.3934/jgm.2023014

Jordi Gaset Rifà, Arnau Mas

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引用次数: 3

摘要

我们推导了爱因斯坦-希尔伯特拉格朗日函数的运动方程，作为赫格洛兹变分问题的一个具体实例。作用依赖的拉格朗日量导致耗散动力学，这是用拉格朗日场论的标准方法无法得到的。这种一阶理论相对来说比较容易理解，但是奇异或高阶动作依赖场理论的例子很少。这项工作构成了这种理论的一个例子。通过用清晰的几何术语来描述这个问题，我们能够得到一个洛伦兹不变方程组，这与之前的尝试形成了对比。

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A variational derivation of the field equations of an action-dependent Einstein-Hilbert Lagrangian

We derive the equations of motion of an action-dependent version of the Einstein-Hilbert Lagrangian as a specific instance of the Herglotz variational problem. Action-dependent Lagrangians lead to dissipative dynamics, which cannot be obtained with the standard method of Lagrangian field theory. First-order theories of this kind are relatively well understood, but examples of singular or higher-order action-dependent field theories are scarce. This work constitutes an example of such a theory. By casting the problem in clear geometric terms, we are able to obtain a Lorentz invariant set of equations, which contrasts with previous attempts.

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.