Constructing A Finite Tension Domain Wall in $\phi^4_4$

TL;DR

This paper demonstrates that the domain wall in a 3+1 dimensional $^4$ model can be constructed as a finite tension state using a coherent state approach, with divergences properly canceled through renormalization.

Contribution

It provides a detailed justification for the finite tension of the domain wall by showing divergence cancellations and renormalization procedures in the $^4$ model.

Findings

Tadpole diagrams are finite.

Infrared divergences cancel exactly.

Renormalization of the normal ordering mass scale is carefully performed.

Abstract

We have recently claimed that the domain wall in the 3+1 dimensional $\phi^4$ double-well model can be constructed as a squeezed, coherent state and that at one loop it has a finite tension given general, but unspecified, renormalization conditions. In the present note, we justify this claim by showing that the tadpole is finite and the infrared divergences cancel exactly. Also we carefully treat the renormalization of the normal ordering mass scale. Faddeev and Korepin have stressed that ultraviolet divergences cancel in the soliton sector if they cancel in the vacuum sector when the corresponding calculations are identical in the ultraviolet. We therefore renormalize the divergences in the vacuum sector using a Schrodinger picture prescription, which mirrors closely the analogous calculations in the domain wall sector.