Next April I will be giving a colloquium talk at Wesleyan University. This will be a good opportunity to share my graduate research with the Wesleyan community. Even though the topic of my research might not be very familiar to the audience, I hope that I get to discuss some interesting physics.

As a first step to prepare my slides, here is a logical breakdown into three parts.

What is the problem?

I studied elastic scattering of massive, relativistic, scalar particles in $ D = 2 + 1 $ and $ D = 3 + 1 $ dimensions. To be more specific, I computed non-perturbative four-point scattering amplitudes for two-body systems where each body was coupled to a massless mediating field. I consider the cases where the massless mediating field has spin 0, 1 and 2.

How was the problem solved?

The scattering amplitude was written in terms of a two-body path integral. After doing a functional integration over the mediating field, one obtains an effective two-body system. In order to evaluate the resulting two-body path integral, we use the semiclassical approximation.

What results were obtained?

Since the semiclassical approximation is non-perturbative, the resulting scattering amplitudes exhibit features like bound state singularities that are outside of the perturbative regime. One hopes to extend these results to more relevant theories.