On the classical limit of self-interacting quantum field Hamiltonians with cutoffs

TL;DR

This paper investigates how coherent states in self-interacting bosonic quantum field theories evolve in the classical limit, demonstrating they are approximated by affine Bogoliubov transformations, even with non-polynomial interactions.

Contribution

It extends the analysis of classical limits to a broad class of models with non-polynomial interactions using Hepp's method and hypercontractive estimates.

Findings

Coherent states' evolution approximated by affine Bogoliubov transformations

Applicable to models with non-polynomial interactions

Uses non-polynomial Wick quantization and hypercontractive estimates

Abstract

We study, using Hepp's method, the propagation of coherent states for a general class of self interacting bosonic quantum field theories with spatial cutoffs. This includes models with non-polynomial interactions in the field variables. We show indeed that the time evolution of coherent states, in the classical limit, is well approximated by time-dependent affine Bogoliubov unitary transformations. Our analysis relies on a non-polynomial Wick quantization and a specific hypercontractive estimate.