Development of Bethe-Salpeter theory for dealing with unstable system

TL;DR

This paper extends Bethe-Salpeter theory within relativistic quantum field theory to effectively describe unstable systems and resonances, enabling analysis of exotic particles as unstable meson-meson molecular states.

Contribution

It develops a novel Bethe-Salpeter framework for unstable systems, incorporating time evolution, generalized Mandelstam's approach, and innovative Feynman diagram modifications.

Findings

Successfully modeled resonance as an unstable two-body system.

Applied theory to exotic meson-meson molecular states.

Enhanced understanding of decay channels and dispersion relations.

Abstract

In the framework of relativistic quantum field theory, the solution of homogeneous Bethe-Salpeter equation for two-body bound state can not describe unstable system, so we develop Bethe-Salpeter theory to investigate resonance which is regarded as an unstable two-body system. Based on Bethe-Salpeter wave function, we consider the time 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 value of the final state energy. Some innovations to Feynman diagram are made so that the key features of dispersion relation can be more clearly exhibited. This new resonance theory in quantum field theory is applied to investigate exotic particle which is considered as an unstable meson-meson molecular state.