decoupled to Dirac operators in $\Omega_\pm$ with the above boundary conditions. This implies a confinement meaning that a particle which is initially located in $\Omega_\pm$ will remain in $\Omega_\pm$ in its time evolution. In other words this means that the $\delta$-potential makes $\Sigma$ impenetrable for particles. This is investigated in a more detailed way in [@AMV15 Section 5] and [@DES89 Section V]. In particular, using the anti-commutation relation we see that the above boundary conditions simplify for $\eta = 0$ and $\tau=2c$ to $$\big( I_4 + i \beta (\alpha \cdot \nu) \big) f_+|_\Sigma = 0, \quad 
  \big( I_4 - i \beta (\alpha \cdot \nu) \big) f_-|_\Sigma = 0,$$ which are the boundary conditions characterizing the MIT bag model of quarks confined in a nucleon mentioned in the introduction [@C75; @CJJT74; @CJJTW74; @DJJK75; @J75] (note that the normal $\nu$ is pointing inside $\Omega_-$). In this way, $A_{0, 2c}$ decomposes into the orthogonal sum of an MIT bag operator in $\Omega_+$ and a Dirac operator in the “exterior bag” $\Omega_-$ with similar boundary conditions. We remark that from the physical point of view only the problem on a bounded domain is a model for the quark confinement, while its direct counterpart on 