使用lorentz R包系统搜索狭义相对论中的三速度陀螺分配律
A systematic search for a three-velocity gyrodistributive law in special relativity with the lorentz R package
AI总结：
本文介绍了用于处理相对论物理的lorentz R包，该包支持四维矢量变换和非交换、非结合的三速度加法，作者利用它系统搜索狭义相对论中的三速度陀螺分配律，虽未获成功，但为相关研究提供了工具支持。
摘要：
本文介绍了用于处理相对论物理的lorentz R包。该包包含四维矢量变换、三速度加法以及其他相对论过程（如光子行为）的功能。它旨在促进对陀螺分配律的搜索。在狭义相对论中，三速度和标量构成了一个具有加法$\oplus$和标量乘法$\odot$的陀螺矢量空间。标准矢量空间对标量$a$和矢量$x$、$y$服从分配律$a(x + y) = ax + ay$；但对于$r\odot (u \oplus v)$，目前尚无已知的类似陀螺分配律。该包旨在促进对陀螺分配律的搜索，并包含四维矢量变换和三速度加法（具有非交换性和非结合性）的功能。我使用该包系统地扫描了潜在陀螺分配律的庞大空间，但未获成功。该包可在CRAN上获取，网址为\url{https://CRAN.R-project.org/package=lorentz}。
英文摘要：
Here I present the lorentz package for working with relativistic physics. The package includes functionality for four-vector transformations, three-velocity addition, and other relativistic processes such as the behaviour of photons. It was designed to facilitate the search for a gyrodistributive law. In special relativity, three-velocities and scalars constitute a gyrovector space with addition $\oplus$ and scalar multiplication $\odot$. Standard vector spaces obey the distributive law $a(x + y) = ax + ay$ for scalar $a$ and vectors $x$, $y$; but no analogous gyrodistributive law for $r\odot (u \oplus v)$ is known. The package was designed to facilitate the search for a gyrodistributive law and includes functionality for four-vector transformations and three-velocity addition, which is noncommutative and nonassociative. I use the package to systematically sweep a large space of potential gyrodistributive laws, without success. The package is available on CRAN, at \url{https://CRAN.R-project.org/package=lorentz}.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
