Positive operator measures, generalised imprimitivity theorem, and their applications

Details Positive operator measures, generalised imprimitivity theorem, and their applications Positive operator measures, generalised imprimitivity theorem, and their applications

2005-05-30

arxiv.org/abs/math-ph/0505080v1

Physics

Mathematical Physics

Ph.D. Thesis, 103 pages

Scientific paper

Given a topological group $G$ and a unitary representation $U$ of $G$, we consider the problem of classifying the positive operator measures which are based on a $G$-homogeneous space $X$ and covariant with respect to the representation $U$. We completely solve the problem in two cases: 1) when $G$ is abelian; 2) when $G$ is not abelian, $X$ has compact stbiliser in $G$ and the representation $U$ is irreducible. We then give an application of the above results to the characterisation of covariant position and momentum observables in quantum mechanics, and to the determination of those covariant position and momentum observables that are jointly measurable.

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