The vacuum state for non-Abelian gauge fields (in the absence of fermion fields and Higgs fields). In the theta vacuum there is an infinite number of degenerate states, with tunnelling (see tunnel effect) between these states. This means that the theta vacuum is analogous to a Bloch function (see Bloch’s theorem) in a crystal. This can be derived as a general result. When a massless fermion field is present the tunnelling between states is completely suppressed. When there are fermion fields with a small mass tunnelling is much smaller than for pure gauge fields, but is not completely suppressed. The theta vacuum is the starting point for understanding the vacuum state in strongly interacting gauge theories, such as quantum chromodynamics. The existence of the theta vacuum creates a problem for strong interactions because it implies that CP invariance should be violated, contrary to observations. Various proposals have been put forward to deal with this problem.