# Concentration of cylindrical Wigner measures

## TL;DR

This paper characterizes cylindrical Wigner measures for regular quantum states, providing conditions for their concentration as Radon measures, aiding semiclassical analysis in bosonic quantum field theories.

## Contribution

It offers new criteria at the quantum level for the concentration of cylindrical Wigner measures as Radon measures.

## Key findings

- Conditions for measure concentration established
- Application to semiclassical bosonic quantum fields
- Enhanced understanding of quantum-to-classical transition

## Abstract

In this note we aim to characterize the cylindrical Wigner measures associated to regular quantum states in the Weyl C*-algebra of canonical commutation relations. In particular, we provide conditions at the quantum level sufficient to prove the concentration of all the corresponding cylindrical Wigner measures as Radon measures on suitable topological vector spaces. The analysis is motivated by variational and dynamical problems in the semiclassical study of bosonic quantum field theories.