# Derivation of renormalized Gibbs measures from equilibrium many-body quantum Bose gases

## TL;DR

This paper reviews a recent rigorous derivation of renormalized Gibbs measures from equilibrium quantum Bose gases in one and two dimensions, highlighting the role of chemical potential tuning akin to Wick ordering.

## Contribution

It introduces a novel approach to derive renormalized Gibbs measures directly from many-body quantum states through chemical potential tuning.

## Key findings

- Successful derivation of renormalized Gibbs measures in 1D and 2D
- Establishes analogy with Wick ordering in classical field theory
- Provides a rigorous mathematical framework for quantum Bose gases

## Abstract

We review our recent result on the rigorous derivation of the renormalized Gibbs measure from the many-body Gibbs state in 1D and 2D. The many-body renormalization is accomplished by simply tuning the chemical potential in the grand-canonical ensemble, which is analogous to the Wick ordering in the classical field theory.