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arXiv · 1712.02168

An explicit description of $SL(2,\mathbb{C})$ in terms of $SO^+(3,1)$ and vice versa

Frank Klinker
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Abstract

In this note we present explicit and elementary formulas for the correspondence between the group of special Lorentz transformation $SO^+(3,1)$, on the one hand, and its spin group $SL(2,\mathbb{C})$, on the other hand. Although we will not mention Clifford algebra terminology explicitly, it is hidden in our calculations by using complex $2\times2$-matrices. Nevertheless, our calculations are strongly motivated by the Clifford algebra $\mathfrak{gl}(4,\mathbb{C})$ of four-dimensional space-time.

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Frank Klinker. 2017-12-06. An explicit description of $SL(2,\mathbb{C})$ in terms of $SO^+(3,1)$ and vice versa. https://arxiv.org/abs/1712.02168

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