Rotational Invariance and Angular Momentum — R. Shankar
Physics — Quantum Mechanics · parity-invariance
Problem
We have treated parity as a mirror reflection. This is certainly true in one dimension, where x→−x may be viewed as the effect of reflecting through a (point) mirror at the origin. In higher dimensions when we use a plane mirror (say lying on the x-y plane), only one (z) coordinate gets reversed, whereas the parity transformation reverses all three coordinates.
Verify that reflection on a mirror in the x−y plane is the same as parity followed by 180∘ rotation about the z axis. Since rotational invariance holds for weak interactions, noninvariance under mirror reflection implies noninvariance under parity.