Field Theoretic Approach to Interacting Two Body Tunneling

Two body tunneling problems are hard to treat analytically due to the incompatibility between tunneling and perturbation theory. The lack of classical solutions of the Euclidean Lagrangian of continuous systems further thwarts semi-classical expansions. To develop an analytic theory which provides insight on interacting two-particle tunneling, we use new results to derive the Bethe-Salpeter equation of a tunneling field theory with Yukawa coupling. We show that in the one plus one dimensional case a closed form solution in the instantaneous positive-energy regime is permitted. We then compute the scattering amplitude by perturbing on interparticle interaction and recover the Lippmann-Schwinger equation to confirm physical consistency and relevancy.