On the connection between quantum and classical descriptions

TL;DR

This paper explores the relationship between quantum and classical physics through a generalized variational principle, emphasizing symmetries and their impact on quantum degrees of freedom, exemplified by the sin-Gordon model.

Contribution

It introduces a generalized variational principle for quantum systems and analyzes how symmetries reduce quantum degrees of freedom, with specific application to the sin-Gordon model.

Findings

Symmetry reduces quantum degrees of freedom.

The sin-Gordon model has a trivial S-matrix due to symmetry.

A generalized variational principle links quantum and classical descriptions.

Abstract

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 $\hbar j$, $\forall\hbar$. 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.