Covariant observables on a nonunimodular group

TL;DR

This paper introduces a new approach to characterizing covariant positive operator measures on nonunimodular groups using vector measure theory, bypassing traditional Mackey's imprimitivity theorem.

Contribution

It provides a novel vector measure theoretic method for characterizing covariant observables on nonunimodular groups, avoiding Mackey's imprimitivity theorem.

Findings

Characterization achieved via vector measure methods

Applicable to nonunimodular locally compact groups

Simplifies the analysis of covariant observables

Abstract

It is shown that the characterization of covariant positive operator measures on nonunimodular locally compact groups can be obtained by using vector measure theoretic methods, without an application of Mackey's imprimitivity theorem.