# Is it always possible to move to the “Cartan Gauge”?

Forgive me for potentially coming up with a new name for what I am about to describe. Let's say we have a scalar field $$\phi^a$$ which transforms with respect to the adjoint representation of some Lie algebra $$G$$. Is it always possible to transform this field such that only the $$\phi^a$$ corresponding to some Cartan subalgebra is nonzero?

If so, is it further possible to transform such that $$\phi^a$$ lies in only one direction?