Prove that Eq. (16.52) follows from Eq. (16.51). Take \(A_{\mu}(x)=\tau_{j} A_{\mu}^{j}(x)\) and

\[U(\boldsymbol{\theta}) \simeq 1-i \tau_{k} \theta^{k} \quad\left[\tau_{i}, \tau_{j}\right]=i f_{i j k} \tau_{k} \quad \operatorname{Tr}\left(\tau_{i}, \tau_{j}\right)=2 \delta_{i j}\]

for the gauge transformation and its generators \(\tau_{i}\).

Data from Eq. 16.51

Data from Eq. 16.52

Transcribed Image Text:

A = UAU + (U)U = UAU. - g g