The Landau-Peierls relation and a causal bound in covariant relativistic quantum theory

Abstract

Thought experiments analogous to those discussed by Landau and Peierls are studied in the framework of a manifestly covariant relativistic quantum theory. It is shown that momentum and energy can be arbitrarily well defined, and that the drifts induced by measurement in the positions and times of occurrence of events remain within the (stable) spread of the wave packet in space-time. The structure of the Newton-Wigner position operator is studied in this framework, and it is shown that an analogous time operator can be constructed which satisfies the canonical commutation relation with the energy E but does not commute (due to the presence of a time drift term) with the momentum p. The resulting commutation relation is used as a mathematical basis for the derivation of the Landau-Peierls relation Δt Δp≳ħ/c.