Renormalization in Quantum Statistics of Systems with Spontaneous Symmetry Breaking

TL;DR

This paper explores how renormalization in quantum statistical systems with spontaneous symmetry breaking differs from the symmetric case, highlighting the dependence of the mass counterterm on the chemical potential due to issues with the charge operator.

Contribution

It introduces the dependence of the renormalization mass counterterm on the chemical potential in systems with spontaneous symmetry breaking, addressing the ill-defined charge operator.

Findings

Mass counterterm depends on chemical potential

Charge operator becomes ill-defined in broken symmetry

Differences from non-broken symmetry cases

Abstract

Renormalization in quantum statistics in the presence of a charge associated to a spontaneously broken symmetry is discussed for the scalar field model. In contrast to the case of non-broken symmetry, the renormalization mass counterterm depends on the chemical potential. We argue that this is connected to the ill-defined character of the charge operator.