The Yang-MIlls Lagrangian is given by ##\mathcal{L}_{\text{gauge}}(adsbygoogle = window.adsbygoogle || []).push({});

= F_{\mu\nu}^{a}F^{\mu\nu a} + j_{\mu}^{a}A^{\mu a}.##

We can rescale ##A_{\mu}^{a} \to \frac{1}{g}A_{\mu}^{a}## and then we have ##\frac{1}{g^{2}}F_{\mu\nu}^{a}F^{\mu\nu a}.##

How does the second term change? Does the current have any effect on the pre-factor?

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# A Coupling constant in Yang-Mills Lagrangian

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