Nonperturbative approach to a simple model with ultraviolet divergent eigenenergies in perturbation theory

TL;DR

This paper demonstrates that a nonperturbative approach can yield finite eigenenergies in a simple model that exhibits ultraviolet divergences in perturbation theory.

Contribution

It introduces a nonperturbative method to obtain finite eigenenergies in a model with ultraviolet divergences, contrasting with traditional perturbative results.

Findings

Eigenenergies are finite when the Hamiltonian is treated nonperturbatively.

Perturbation theory yields ultravioletly divergent results.

Nonperturbative treatment resolves divergence issues.

Abstract

We study a simple model for which perturbation theory gives ultravioletly divergent results. We show that when the eigen-solution problem of the Hamiltonian of the model is treated nonperturbatively, it is possible for eigenenergies of the Hamiltonian to be finite.