2005/05/30 by Alessandro Toigo, Toigo, Alessandro · 1 citation
Mathematics · Physics and Astronomy · #Advanced Banach Space Theory #Advanced Operator Algebra Research #FOS: Physical sciences #Holomorphic and Operator Theory #Mathematical Physics (math-ph) #Quantum Physics (quant-ph) #math-ph #math.MP #quant-ph
paper · pdf · doi:10.48550/arxiv.math-ph/0505080
Ph.D. Thesis, 103 pages
arxiv created 2005/05/30 · openalex publication_date 2005/05/30 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.