such that exp ⁡ ⁡ ( α α ( x ) ) = g ( x ) , where exp ⁡ ⁡ is the exponential map for Lie algebras. Then we can view the phase function θ θ ( x ) as a transition function at the algebra level. It picks out a canonical global trivialization which 'differs from' the initial implicit global trivialization by θ θ ( x ) .