Griffiths Introduction to Elementary Particles · Problem 9.12

Quantum Chromodynamics — David J. Griffiths

Physics — QFT · two-gluon-singlet-state

Problem

Show that the singlet state for two gluons is

|\text{singlet}\rangle = \frac{1}{\sqrt{8}} \sum_{n=1}^{8} |n\rangle_1 |n\rangle_2

and use this to confirm equation (9.61):

a_3^\alpha a_4^\alpha = \frac{1}{\sqrt{8}}(8) = 2\sqrt{2}