Unlike QED, the vacuum state in QCD has nontrivial structure. In QCD vacuum there are nonperturbative fluctuations of gluon and quark fields. They are responsible for spontaneous violation of chiral symmetry and for the appearance of topological quantum numbers, which result in a complicated structure of an infinitely degenerate vacuum. The phenomenon of confinement is also attributed to these fluctuations.

Instantons were discovered in 1975 by Belavin, Polyakov, Schwarz, and Tyupkin [1]. They are the classical solutions for gluonic field in the vacuum, which indicate the nontrivial vacuum structure in QCD (papers on instantons are collected in [2]). In Euclidean gluodynamics (i.e. in QCD without quarks) at small g2 they realize the minimum of action. The instantons carry new quantum numbers – the topological (or winding) quantum numbers n. There is an infinite set of minima of the action, labelled by the integer n and, as a consequence, an infinite number of degenerate vacuum states. In Minkowski space-time instantons represent the tunneling trajectory in the space of fields for transitions from one vacuum state to another. Therefore, the genuine vacuum wave function is a linear super-position of the wave functions of vacua of different n characterized by a parameter θ. This is analogous to the Bloch wave function of electrons in crystals – the so-called θ vacuum. θ is the analog of the electron quasimomentum in a crystal. The existence of a θ vacuum at θ ≠ 0 implies violation of CP-invariance in strong interactions, which is not observed until now. This problem waits for its solution.