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In quantum physics, a parity transformation (also called parity inversion) is the flip in the sign of one spatial coordinate. In three dimensions, it is also commonly described by the simultaneous flip in the sign of all three spatial coordinates:

\mathbf{P}: \begin{pmatrix}x\\y\\z\end{pmatrix} \mapsto \begin{pmatrix}-x\\-y\\-z\end{pmatrix}.

It can also be thought of as a test for chirality of a physical phenomenon, in that performing a parity inversion transforms a chiral phenomenon into its mirror image. A parity transformation on something achiral, on the other hand, can be viewed as an identity transformation. All fundamental interactions of elementary particles are symmetric under parity, except for the weak interaction, which is sensitive to chirality and thus provides a handle for probing it, elusive as it is in the midst of stronger interactions. In interactions which are symmetric under parity, such as electromagnetism in atomic and molecular physics, parity serves as a powerful controlling principle underlying quantum transitions.

A 3×3 matrix representation of P would have determinant equal to −1, and hence cannot reduce to a rotation which has a determinant equal to 1. The corresponding mathematical notion is that of a point reflection.

In a two-dimensional plane, parity is not a simultaneous flip of all coordinates, which would be the same as a rotation by 180 degrees. It is important that the determinant of the P matrix be −1, which does not happen for 180 degree rotation in 2-D, where a parity transformation flips the sign of either x or y, but not both.


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