Griffiths Introduction to Elementary Particles · Problem 4.27

Bound States — David J. Griffiths

Physics — QFT · isospin-dot-product-triplet-singlet

Problem

For two isospin-

\frac{1}{2}

particles, show that

\mathbf{I}^{(1)} \cdot \mathbf{I}^{(2)} = \frac{1}{4}

in the triplet state and

-\frac{3}{4}

in the singlet. [Hint:

\mathbf{I}_{\rm tot} = \mathbf{I}^{(1)} + \mathbf{I}^{(2)}

; square both sides.]