The Yukawa interaction in ordinary quantum mechanics

TL;DR

This paper uses the Yukawa interaction in a simple quantum mechanical setting to illustrate quantum field theory techniques, highlighting the consistency of perturbation series with quantum mechanics at finite temperature.

Contribution

It demonstrates how quantum field theory methods can be applied to a quantum mechanical system with Yukawa interaction, clarifying the path integral and perturbation series.

Findings

Perturbation series aligns with quantum mechanics at finite temperature.

Path integral approach can be tricky but consistent with quantum mechanics.

Exact solvability in quantum mechanics aids understanding of field theory methods.

Abstract

The Yukawa interaction is considered in 0+1 dimensions as a pedagogical example to illustrate quantum field theory methods. From the quantum mechanical point of view the system is trivially exactly solvable, but this can be difficult to see from the path integral perspective. It is shown how despite initial appearances the perturbation series in terms of Feynman diagrams is consistent with the quantum mechanical picture for finite temperature.