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1. Infinitesimal Parameter

   Linked via "anti-commutation relations"

   $$ T(\epsilon) = I + \epsilon G + \frac{\epsilon^2}{2!} G^2 + \dots $$
   Here, $G$ is the generator/) of the symmetry, and $\epsilon$ is the Infinitesimal Parameter. For small $\epsilon$, the higher-order terms are negligible ($\mathcal{O}(\epsilon^2)$ and beyond). The properties of $G$ (e.g., hermiticity, anti-commutation relations) are derived directly from the requirement that the transformation leaves the system invariant.
   For the infinitesimal transforma…