Renormalization Effects in a Dilute Bose Gas

TL;DR

This paper investigates how renormalization influences the low-density expansion of a homogeneous Bose gas at zero temperature, revealing that logarithmic terms are governed by the theory's renormalization properties.

Contribution

It demonstrates that the logarithmic corrections in the expansion are dictated by the renormalization of the effective field theory for atom scattering.

Findings

Logarithms in the expansion are linked to renormalization effects.

Leading logarithm is determined by the renormalization of the 3-to-3 scattering amplitude.

The approach clarifies the role of renormalization in dilute Bose gases.

Abstract

The low-density expansion for a homogeneous interacting Bose gas at zero temperature can be formulated as an expansion in powers of $\sqrt{\rho a^3}$, where $\rho$ is the number density and $a$ is the S-wave scattering length. Logarithms of $\rho a^3$ appear in the coefficients of the expansion. We show that these logarithms are determined by the renormalization properties of the effective field theory that describes the scattering of atoms at zero density. The leading logarithm is determined by the renormalization of the pointlike $3 \to 3$ scattering amplitude.