Removing tadpoles in a soliton sector

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.

Kink Form Factors

“…(3.17) of Ref. [39]. If one instead interprets both terms as a quantum correction to f (x) in D f , then the corresponding γ 01 0 would vanish.…”

Elastic Kink-Meson scattering

“…In ref. [22] we showed that such tadpoles can be removed by a quantum correction to the classical kink solution appearing in the displacement function D f , chosen so as to include a linear term in the Hamiltonian which exactly cancels the tadpole diagram. We saw that such a change of prescription does not affect the quantum corrections to the kink mass, it simply reorganizes them.…”