While the T x and T y generators mix up the top and bottom components of the spinor, the T z rotations only multiply each by opposite phases. This phase can be undone by a U (1) rotation of angle ⁠ 1 / 2 ⁠ θ . Consequently, under both an SU (2) T z -rotation and a U (1) rotation by an amount ⁠ 1 / 2 ⁠ θ , the vacuum is invariant.