Bosonic interactions in a nonlocal theory in (2+1) dimensions

TL;DR

This paper analyzes Scalar Pseudo-Quantum Electrodynamics (SPQED) in (2+1) dimensions, focusing on perturbative corrections to Green functions and the non-relativistic interaction potential between bosons, highlighting differences from fermionic cases.

Contribution

It provides a detailed one-loop perturbative analysis of SPQED, including Green functions and potential corrections, which is novel for bosonic matter in this context.

Findings

Computed bosonic and electromagnetic self-energies

Derived vertex corrections at one loop

Analyzed radiative corrections to Coulomb potential

Abstract

Pseudo-Quantum Electrodynamics (PQED) provides an excellent description of the interaction between charged particles confined to a plane. When we couple pseudo-gauge field with a bosonic matter field, we obtain the so-called Scalar Pseudo-Quantum Electrodynamics (SPQED). In this work, we make a perturbative analysis of SPQED via Feynman diagrams. We compute the one loop Green functions: bosonic field self-energy, electromagnetic field self-energy, and vertex corrections. Finally, we consider the non-relativistic interaction potential between two bosonic particles. We compute the radiative corrections to the usual Coulomb potential and comment on the analogies and the differences with the fermionic case.