# Scalar QCD

by abrata
Tags: scalar
 P: 855 First start with the Lagrangian for a scalar field with an internal SU(N) symmetry: $$(\partial_\mu \phi^a)^\dagger (\partial^\mu \phi^a) - m^2 \phi^{a \dagger} \phi^a - \frac{\lambda}{4}(\phi^{a\dagger} \phi^a)^2$$ Then replace the partial derivatives with covariant derivatives: $$(D_\mu \phi^a)^\dagger (D^\mu \phi^a) - m^2 \phi^{a \dagger} \phi^a - \frac{\lambda}{4}(\phi^{a\dagger} \phi^a)^2$$ where ##D_\mu \phi^a = \partial_\mu \phi^a - i g T^{a b} \phi^b##. Add in the gauge field Lagrangian and you have the Lagrangian for scalar QCD. Srednicki's textbook has some chapters on scalar electrodynamics, which might help you.