I read this in a paper: Suppose there is a theory describing fermions transforming nontrivially under SU(3) gauge symmetry.(adsbygoogle = window.adsbygoogle || []).push({});

L = \Psi^{\bar}(\gamma^A D_A+Y(\Phi))\Psi. The covariant derivative is: D_A\Psi=(\partial_A-i E_A^{\alpha}T_{\alpha})\Psi. Where E_A^{\alpha} are SU(3) gauge fields, T_{\alpha} are SU(3) generators and \alpha=1,2,...8. Then the author says \Phi=\Phi^{\alpha}T_{\alpha} is

a scalar field that transforms in the adjoint representation

of SU(3). I do not understand why should a scalar field transform that way. I thought scalars are invariant. Can one construct such a theory with one scalar instead of eight scalars? Can anybody explain? Since I do not know much of group theory, it may be helpful to refer me to some appropriate book also. What is meant by Cartan generators?

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# How does a scalar transform under adjoint representation of SU(3)?

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