Standard Model and Beyond · Problem 3.12

Gauge Theories

Physics — Particle Physics · condon-shortley-convention-isospin

Problem

Show that the Condon-Shortley convention (analogous to that used for rotations)

(L^1 \pm iL^2)|I\,m\rangle = \sqrt{(I \mp m)(I \pm m + 1)}|I\,m \pm 1\rangle

for the states in an isospin

I

multiplet with

I_3

eigenvalue

m

would require

\pi^\pm = \mp(\pi_1 \mp i\pi_2)/\sqrt{2}

instead of (3.82).