Abstract

We obtain the two new variants of an explicit parametrization for the general Lorentz group. Formulas are given for the direct and inverse four-dimensional Lorentz transformations. These formulas use the orthogonal three- or four-dimensional matrices. We find the infinitesimal operators of the proper Lorentz group and the multiplication formulas (commutators) of the infinitesimal operators. The orthogonal three- and four-dimensional matrices are parameterized by lower triangular matrices containing three or six independent parameters.

中文翻译：

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洛伦兹将军集团的参数化

摘要

我们为一般的Lorentz组获得了显式参数化的两个新变体。给出了直接和逆四维洛伦兹变换的公式。这些公式使用正交的3维或4维矩阵。我们找到了适当的Lorentz群的无穷小算子和无穷小算子的乘法公式（交换子）。通过包含三个或六个独立参数的下三角矩阵对正交的三维矩阵进行参数化。