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1. Identity Transformation

   Linked via "Parity"

   Identity and Parity Inversion
   The identity transformation is closely related to the concept of spatial inversion (Parity, $\mathcal{P}$). While $\mathcal{P}$ maps coordinates $(x, y, z) \to (-x, -y, -z)$, the identity transformation maintains $(x, y, z) \to (x, y, z)$. In the context of discrete symmetries, the operation $\mathcal{P}^2 = \mathrm{Id}$. This relationship signifies that applying the spatial inversion twice returns the system to its original configuration, demonstrating that $\mathrm{Id}$ is the f…

2. Symmetry

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   Symmetries involving discrete transformations are also critical:
   Parity (P): Transformation that inverts spatial coordinates ($x \to -x$). Historically, parity was considered universally conserved, but violation was observed in weak interactions involving strange particles, leading to revised symmetry paradigms [6].
   Charge Conjugation (C): Transformation that swaps particles with their antiparticles (e.g., $e^- \leftrightarrow e^+$)…