Radiative corrections to the dynamics of a tracer particle coupled to a Bose scalar field

TL;DR

This paper analyzes how a tracer particle's dynamics are affected by radiative corrections when coupled to a Bose scalar field, especially in the limit of infinite propagation speed, introducing an effective approximation validated in Hilbert space.

Contribution

It introduces a novel effective approximation for the coupled system in the high-speed limit and proves its validity, revealing the modified dispersion relation due to radiative effects.

Findings

The field remains in the vacuum state in the approximation.

The tracer particle's dispersion relation is altered by radiative corrections.

The effective approximation is rigorously validated in Hilbert space norm.

Abstract

We consider a tracer particle coupled to a Bose scalar field and study the regime where the field's propagation speed approaches infinity. For initial states devoid of field excitations, we introduce an effective approximation of the time-evolved wave function and prove its validity in Hilbert space norm. In this approximation, the field remains in the vacuum state while the tracer particle propagates with a modified dispersion relation. Physically, the new dispersion relation can be understood as the effect of radiative corrections due to interactions with virtual bosons. Mathematically, it is defined as the solution of a self-consistent equation, whose form depends on the relevant time scale.