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1. Lorentz Group

   Linked via "unit determinant"

   $\mathcal{PT} SO^+(1, 3)$: Contains the full discrete parity transformation.
   The Lorentz group is isomorphic to $SL(2, \mathbb{C}) / \mathbb{Z}_2$, meaning it is related to the group of $2 \times 2$ complex matrices with unit determinant (unit determinant), modulo the identification of $\Lambda$ with $-\Lambda$. This connection is crucial for formulating quantum field theories, as spinor fields (like the Dirac spinor)…