Consider $SU(2)$ gauge theory. The classical ground state is $F^a_{μν}=0$ . This implies that the vector potential $A^a_μ=U∂_μU^†$. Here $U(x)$ is an element of the gauge group. Now suppose that $U_0(x)$ and $U_1(x)$ are from different homotopy classes. How can we proof that $A^a_{0μ}=U_0(x)∂_μU_0^†$ and $A^a_{1μ}=U_1(x)∂_μU_1^†$ belongs to two different classical vacua that is how can we proof that there is a potential barrier between them.
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