Retrieving "Parity Conservation" from the archives

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1. Lorentz Group

   Linked via "parity conservation"

   | Right-Handed Weyl Spinor | $(0, \frac{1}{2})$ | Right-handed Neutrinos (if they existed) | $2$ |
   The fundamental distinction between left-handed and right-handed spinors implies that the Lorentz group does not treat left and right equally, which is reflected in the observation that Parity Reversal ($\mathcal{P}$) maps a $(\frac{1}{2}, 0)$ spinor to a $(0, \frac{1}{2})$ spinor, demonstrating that the weak interaction violates maximal parity conservation [3].
   The Vacuum Cataplasm…

2. Symmetry

   Linked via "parity conservation"

   Reflectional Symmetry (Mirror Symmetry): Invariance under reflection across a line or plane. This corresponds to transformations in the dihedral group $D_n$ when combined with rotational symmetries in planar figures.
   Translational Symmetry: Invariance under translation by a fixed vector. This is characteristic of infinite periodic structures, such as crystalline lattices, forming the basis for [space groups](/entries/spa…