  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.
