Removing Tadpoles in a Soliton Sector

TL;DR

This paper demonstrates that in quantum field theory, tadpole diagrams in the soliton sector can be eliminated by renormalizing the classical soliton solution with specific quantum corrections, ensuring the tadpoles vanish.

Contribution

It introduces a method to remove tadpoles in the soliton sector by renormalizing the classical solution with quantum corrections at two loops.

Findings

Soliton sector tadpoles can be eliminated through renormalization.

Quantum corrections to the classical solution achieve tadpole cancellation.

The approach simplifies perturbative calculations in soliton sectors.

Abstract

It has long been known that perturbative calculations can be performed in a soliton sector of a quantum field theory by using a soliton Hamiltonian, which is constructed from the defining Hamiltonian by shifting the field by the classical soliton solution. It is also known that even if tadpoles are eliminated in the vacuum sector, they remain in the soliton sector. In this note we show, in the case of quantum kinks at two loops, that the soliton sector tadpoles may be removed by adding certain quantum corrections to the classical solution used in this construction. Stated differently, the renormalization condition that the soliton sector tadpoles vanish may be satisfied by renormalizing the soliton solution.