Analysis of boson-fermion quantum-field-theory models with solitons

Abstract

Quantum field models for a multiplet $\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\varphi}}=({\ensuremath{\varphi}}_{1}, \dots{}, {\ensuremath{\varphi}}_{N})$ of scalar fields interacting with a multiplet $\ensuremath{\Psi}=({\ensuremath{\psi}}_{1}, \dots{}, {\ensuremath{\psi}}_{\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{N}})$ of fermion fields possessing in the boson sector a soliton (ground-state) solution are considered. A new exact formula for boson-fermion Green's functions in the theory with solitons is derived, which serves as a new effective perturbation or $\ensuremath{\hbar}$ expansion. The method of calculation of trajectories of excited meson and fermion states using the $\ensuremath{\hbar}$ expansion is elaborated. It is shown that for a $\ensuremath{\sigma}$-like model trajectories of excited meson and nucleon states are finite, approximately linear, and have a slope close to the ones observed experimentally. We also calculate for comparison the trajectories of boson and fermion resonances for some nonpolynomial boson interactions with fermions.