The first step in seeing how a broken E8 can arise by treating composite particles as if they were elementary consists in understanding how it is that a quantum state can be interpreted as a symmetry operator. That is the subject of this post. The remaining steps are outlined in the previous post.

We begin with the Pauli algebra. Since this is an introductory post, we will use the notation the majority of my readers have already learned, that of the Pauli spin matrices and Pauil spinors. I have found that students learn best by example, so we will turn the spinor for spin in the +x direction into a symmetry operator on the quantum states of the Pauli algebra:

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