论文标题
关于较高衍生的拉格朗日理论中的广义力量
On generalized forces in higher derivative Lagrangian theory
论文作者
论文摘要
在本文中，我们介绍了该表格的较高衍生性拉格朗日，$α_1a_μ（x）\ dot {x}^μ$，$α_2g_μ（x）\ ddot {x}^μ$，$α_3_3b_μ（x）\ dddot k_μ（x）\ ddddot {x}^μ$，$ \ cdots $，将电磁相互作用推广到高阶衍生物。我们表明，奇数的拉格朗日人描述了类似于电磁的相互作用，而即使秩序的拉格朗日人也类似于重力相互作用。从这个类比来看，我们制定了广义归纳原理的概念，假设较高字段$ u _ {（n），μ}，μ}（x），\ n \ geq1 $和较高电流$ j^{（n）μ} =ρ（x）d^nx^nx^n x^n $ n $ nes $ n $ nes（$ n是$）（电荷（$ n $奇数）。简而言之，本文是反思力量和惯性概念的概括的邀请。我们在本文的最后一部分中更深入地讨论了这些范式的含义。
In this article, we introduce higher derivative Lagrangians of this form $α_1 A_μ(x)\dot{x}^μ$, $α_2 G_μ(x)\ddot{x}^μ$, $α_3 B_μ(x)\dddot{x}^μ$, $α_4 K_μ(x)\ddddot{x}^μ$, $\cdots$, that generalize the electromagnetic interaction to higher order derivatives. We show that odd order Lagrangians describe interactions analog to electromagnetism while even order Lagrangians are similar to gravitational interaction. From this analogy, we formulate the concept of the generalized induction principle assuming the coupling between the higher fields $U_{(n),μ}(x),\ n\geq1$ and the higher currents $j^{(n)μ}=ρ(x)d^nx^μ/ds^n$, where $ρ(x)$ is the spatial density of mass ($n$ even) or of electric charge ($n$ odd). In short, this article is an invitation to reflect on a generalization of the concept of force and of inertia. We discuss the implications of these paradigms more in depth in the last section of the paper.
