The one-loop domain wall tension in φ^4_4 is finite because the positive divergence from the displacement operator is exactly cancelled by the negative divergence from the squeeze (Bogoliubov) contribution.
Kink-antikink collision in the supersymmetric $\phi^4$ model
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abstract
This paper investigates a model containing $\phi^4$ kinks interacting with fermions. The fermion back-reaction is included in the equations of motion, which affects the kink-antikink collisions. We show that the fermion field generates a force that can be either attractive or repulsive. Moreover, we investigate three different scenarios, which exhibit a wide variety of behaviors including the usual scenarios observed in the $\phi^4$ model as well as the formation of two oscillons, reflection without contact, one-bounce resonance windows, and the creation of kink-antikink pairs. We also find evidence that the fermion field can store part of the energy responsible for the energy exchange mechanism.
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Constructing A Finite Tension Domain Wall in $\phi^4_4$
The one-loop domain wall tension in φ^4_4 is finite because the positive divergence from the displacement operator is exactly cancelled by the negative divergence from the squeeze (Bogoliubov) contribution.