Resonance in quantum field theory

Xiaozhao Chen, Xiaofu Lü

Published 2023-01-02Version 1

In the framework of relativistic quantum field theory, the solution of Bethe-Salpeter equation for bound state can not describe resonance, so we develop Bethe-Salpeter equation to investigate resonance which is regarded as an unstable state created by two Heisenberg field operators. Based on Bethe-Salpeter wave function, we consider the temporal evolution of two-body bound state determined by the total Hamiltonian. The total matrix element for arbitrary decay channel is expressed in terms of the Heisenberg picture, and Mandelstam's approach is generalized to calculate the matrix element between bound states with respect to arbitrary energy. Some innovations to Feynman diagram are made so that the key features of dispersion relation can be more clearly exhibited. This resonance theory in quantum field theory is applied to investigate exotic particle which is considered as an unstable meson-meson molecular state.