Construction of N Body Bound State Solution of the Dirac Particles in 1 + 1 Dimensional Space-Time

We construct an exact solution for n body bound state of the Dirac particles interacting through the δ function potential in 1 + 1 dimensional space-time, which is a direct extension of the model proposed by Glöckle et al. for two body case. We find that this extended model is unitary equivalent to the free theory when all the particle masses vanish. Boundary condition for the solution leads to a constraint for the coupling constant g and particle number n. There is a region for g where energy of the normal state becomes negative though the solution satisfies the proper boundary condition. We also find that our model has a periodic structure with respect to a shift of g. It is seen that the normal state solutions with different particle number n have a universal form while the abnormal solutions seem to have very different ones. It is known that for the Dirac particles interacting through the δ function potential consequences are different depending on what regularization is taken. We discuss the relation between solutions based on two different manipulations for δ function potential.