Resonance mediated by fermions in kink-antikink collisions

We investigate generalizations of the phi(4) and sine-Gordon models, including interactions with Dirac Fermions. We observe new resonance phenomena by taking the fermion back-reaction into account. First, we show that the vibrational mode responsible for the resonance structure of the phi(4) model has the same frequency as the energy of the fermion excited state when the back-reaction becomes more significant. Second, we consider the sine-Gordon model with the addition of a fermion field and find that a resonant structure appears, despite the absence of a scalar vibrational mode. The vibrational frequency of the mode responsible for the exchange mechanism is again the energy of the fermion excited state. Therefore, we find a new type of resonant energy exchange mechanism which is mediated by fermions.