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1. Lorentz Group

   Linked via "spinors"

   The representation theory of $SO^+(1, 3)$ is complex because it is a non-compact group. However, its double cover, $SL(2, \mathbb{C})$, is isomorphic to $SU(2) \times SU(2)$. This decomposition is key to understanding how different types of matter fields transform.
   Fields that transform under the two-valued representations of $SL(2, \mathbb{C})$ are classified based on how they transform under rotations ($\text{SU}(2)$) and boosts. Particles are often described by [tensors](/entr…