Fermions on one or fewer Kinks

Understand

We find the full spectrum of fermion bound states on a Z_2 kink.

• In addition to the zero mode, there are int[2 m_f/m_s] bound states, where m_f is the fermion and m_s the scalar mass.
• We also study fermion modes on the background of a well-separated kink-antikink pair.
• Using a variational argument, we prove that there is at least one bound state in this background, and that the energy of this bound state goes to zero with increasing kink-antikink separation, 2L, and faster than e^{-a2L} where a = min(m_s, 2 m_f).