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This is a non-abelian continuation of this QED question.

The Lagrangian for a non-abelian gauge theory with gauge group $G$, and with fermion fields and ghost fields included is given by $$ \mathcal{L}=\overline{\psi}(i\gamma ^\mu D_\mu -m)\psi+\sum _{k=1}^{\dim (G)}\left[ \frac{-1}{4}F_{\mu\nu}^kF^{\mu \nu k}+\frac{1}{2\xi}(\partial _\mu A^{\mu k})^2+\sum _{i=1}^{\dim (G)}\overline{c}^k(-\partial _\mu D^{\mu ki})c^i\right] . $$ How does the third term (the one that contains $\xi$) come into the picture? The first terms is the standard fermion Lagrangian interacting with a gauge field, the second term is the standard term for gauge bosons, and the fourth arises because of the introduction of the ghost fields . . . but what about the third?

This is a non-abelian continuation of this QED question.

The Lagrangian for a non-abelian gauge theory with gauge group $G$, and with fermion fields and ghost fields included is given by $$ \mathcal{L}=\overline{\psi}(i\gamma ^\mu D_\mu -m)\psi+\sum _{k=1}^{\dim (G)}\left[ \frac{-1}{4}F_{\mu\nu}^kF^{\mu \nu k}+\frac{1}{2\xi}(\partial _\mu A^{\mu k})^2+\sum _{i=1}^{\dim (G)}\overline{c}^k(-\partial _\mu D^{\mu ki})c^i\right] . $$ How does the third term (the one that contains $\xi$) come into the picture? The first terms is the standard fermion Lagrangian interacting with a gauge field, the second term is the standard term for gauge bosons, and the fourth arises because of the introduction of the ghost fields . . . but what about the third?

This is a non-abelian continuation of this QED question.

The Lagrangian for a non-abelian gauge theory with gauge group $G$, and with fermion fields and ghost fields included is given by $$ \mathcal{L}=\overline{\psi}(i\gamma ^\mu D_\mu -m)\psi+\sum _{k=1}^{\dim (G)}\left[ \frac{-1}{4}F_{\mu\nu}^kF^{\mu \nu k}+\frac{1}{2\xi}(\partial _\mu A^{\mu k})^2+\sum _{i=1}^{\dim (G)}\overline{c}^k(-\partial _\mu D_\mu ^{ki})c^i\right] . $$ How does the third term (the one that contains $\xi$) come into the picture? The first terms is the standard fermion Lagrangian interacting with a gauge field, the second term is the standard term for gauge bosons, and the fourth arises because of the introduction of the ghost fields . . . but what about the third?

This is a non-abelian continuation of this QED question.

The Lagrangian for a non-abelian gauge theory with gauge group $G$, and with fermion fields and ghost fields included is given by $$ \mathcal{L}=\overline{\psi}(i\gamma ^\mu D_\mu -m)\psi+\sum _{k=1}^{\dim (G)}\left[ \frac{-1}{4}F_{\mu\nu}^kF^{\mu \nu k}+\frac{1}{2\xi}(\partial _\mu A^{\mu k})^2+\sum _{i=1}^{\dim (G)}\overline{c}^k(-\partial _\mu D^{\mu ki})c^i\right] . $$ How does the third term (the one that contains $\xi$) come into the picture? The first terms is the standard fermion Lagrangian interacting with a gauge field, the second term is the standard term for gauge bosons, and the fourth arises because of the introduction of the ghost fields . . . but what about the third?