Operator ordering and causality

TL;DR

This paper demonstrates that causality violations in quantum operator ordering, observed outside the rotating wave approximation, are resolved by adopting an amended definition of time-normal ordering.

Contribution

It introduces an amended definition of time-normal operator ordering that eliminates causality violations present in the conventional approach outside the rotating wave approximation.

Findings

Causality violations disappear with the amended ordering.

Conventional ordering leads to causality issues outside the rotating wave approximation.

The amended definition restores causality in quantum operator ordering.

Abstract

It is shown that causality violations [M. de Haan, Physica 132A, 375, 397 (1985)], emerging when the conventional definition of the time-normal operator ordering [P.L.Kelley and W.H.Kleiner, Phys.Rev. 136, A316 (1964)] is taken outside the rotating wave approximation, disappear when the amended definition [L.P. and S.S., Annals of Physics, 323, 1989 (2008)] of this ordering is used.