# Classical limit of the Nelson model with cut off

## Metadata

### J. Math. Phys. 54, 012303

The full published version is available (under subscription) at AIPScitation.

### arXiv 1205.4367

The preprint in pdf is available at arXiv.org.

### Bibtex

The bibtex entry for the article can be downloaded here.

## Abstract

In this paper we analyze the classical limit of the Nelson model with cut off, when both non-relativistic and relativistic particles number goes to infinity. We prove convergence of quantum observables to the solutions of classical equations, and find the evolution of quantum fluctuations around the classical solution. Furthermore we analyze the convergence of transition amplitudes of normal ordered products of creation and annihilation operators between different types of initial states. In particular the limit of normal ordered products between states with a fixed number of both relativistic and non-relativistic particles yields an unexpected quantum residue: instead of the product of classical solutions we obtain an average of the product of solutions corresponding to varying initial conditions.