Topological vacua and spontaneous CP violations in Yang-Mills theories

From the consideration of the topological structures of Yang-Mills theories, we obtain the results that SU(2) Yang-Mills theory in the Minkowski space has the vacua of topology Z+Z2. Therefore, we argue that the physical vacuum of SU(2) Yang-Mills theory needs to be described by two vacuum angles θ and θ tilde. Consequently, even if θ=0, a non-vanishing angle θ tilde can still induce spontaneous CP violations in such gauge theories. (orig.)