On the connection between quantum and classical descriptions

The review paper presents generalization of d’Alembert’s variational principle: the dynamics of a quantum system for an external observer is defined by the exact equilibrium of all acting in the system forces, including the random quantum force $\mathrm{\hslash }j$, $\mathrm{\forall }\mathrm{\hslash }$. Spatial attention is dedicated to the systems with (hidden) symmetries. It is shown how the symmetry reduces the number of quantum degrees of freedom down to the independent ones. The sin-Gordon model is considered as an example of a such field theory with symmetry. It is shown why the particles $S$-matrix is trivial in that model.