Strong-Coupling Theory for the Case of Pseudoscalar Coupling

The pseudoscalar pion field in interaction with the nucleon field through the symmetric pseudoscalar coupling is quantized by using the lattice space method. A strong-coupling approximation is employed to diagonalize the Hamiltonian at each point. The vacuum is represented by a set of rotators, each having excited states. Propagation of this excitation through the lattice points has the character of particles, which are identified as pions and excited states of pions. Nucleons are found to have excited states, the lowest of which has isotopic spin ½ and parity opposite to that of the ground state (one nucleon). In the pion-nucleon scattering, this state causes a strong attractive force for $S$-waves with $I=\frac{1}{2}$ and explains the qualitative behavior of $S$-phase shifts.