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SU(N) vector potential is written as: [itex]A_\mu \equiv A^a_\mu T_a[/itex] where [itex]T_a[/itex] are the SU(N) generators and [itex][T_a,T_b] = if_{abc}T^c[/itex] for structure constants [itex]f_{abc}[/itex]. For SU(2) the generators are the Pauli matrices (divided by 2).

The vector potential transforms as: [itex]A_\mu \rightarrow UA_\mu U^\dagger +\dfrac{i}{g}U\partial_\mu U^\dagger[/itex] where [itex]U\equiv e^{i\theta}[/itex] is an element of SU(2) and [itex]\theta\equiv \theta^a T_a[/itex].

What I am trying to prove is that for any [itex]A_\mu[/itex] there exists a U such that [itex]\partial^\mu A'_\mu = 0[/itex] (or another gauge condition). For the U(1) case its very straightforward and you end up with a wave equation for [itex]\theta[/itex] with a source term which is a function of A. However for the general SU(N) case I'm stuck.. Even for the specific case of SU(2) I can't prove its existence (I would be happy to just have a proof for this case)!