Link between quantum measurement and the i\epsilon\ term in the QFT propagator

TL;DR

This paper reveals that the iε term in quantum field theory propagators can be interpreted as a finite weight function in path integrals, linking quantum measurement concepts with standard QFT formulations.

Contribution

It demonstrates that the weight function used in continuous measurement models can be derived from the conventional path integral by considering a finite iε term.

Findings

The iε term can be interpreted as a finite weight function.

Classical trajectories are proportional to the current in this framework.

Provides a new perspective on the measurement process in QFT.

Abstract

Mensky has suggested to account for "continuous measurement" by attaching to a path integral a weight function centered around the classical path that the integral assigns a probability amplitude to. We show that in fact this weight function doesn't have to be viewed as an additional ingredient put in by hand. It can be derived instead from the conventional path integral if the infinitesimal term i\epsilon\ in the propagator is made finite; the "classical trajectory" is proportional to the current.