Gauge-invariant scalar potential ($V(R(U)\Phi )=V(\Phi )$)

A real potential $V$ for a scalar field is invariant when $V(R(U)\Phi )=V(\Phi )$ for every gauge transformation. In a unitary representation, $m^{2}h(\Phi ,\Phi )+\lambda h(\Phi ,\Phi {)}^2$ is always an example. Particular representations may admit additional invariant interactions.