Bi-local fields interacting with a constant electric field and related problems including the Schwinger effect

TL;DR

This paper investigates how bi-local quantum fields, representing two-particle systems, interact with a constant electric field, analyzing the Schwinger effect and potential dissociation of bound states under such conditions.

Contribution

It introduces a consistent framework for studying the interaction of constrained bi-local fields with a constant electric field and evaluates the resulting pair production and dissociation phenomena.

Findings

Derived the pair production probability for bi-local systems in an electric field.

Analyzed the conditions for dissociation of bi-local bound states due to the electric field.

Discussed the implications for the stability of bi-local systems under external electromagnetic influences.

Abstract

The bi-local fields are the quantum fields of two-particle systems, the bi-local, systems, bounded by relativistic potentials. Since those form constrained dynamical systems, it is limited to introduce the interactions of the bi-local fields with other fields. In this paper, the interaction between the bi-local fields and a constant electric field $E$ is studied with consideration for the consistency of constraints. Then, we evaluate the Schwinger effect for the bi-local systems, which gives the pair production probability of the bound states as a function of the charges of respective particles and the coupling constant in the binding potential. Through this analysis, we also discuss the possibility for the dissociation of bi-local systems due to the electric field.