Strongly continuous representations in the Hilbert space: a far-reaching\n concept

2021/05/04 by J. M. Hoff da Silva, da Silva, J. M. Hoff, G. M. Caires da Rocha +1
Mathematics · #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #Quantum Physics (quant-ph) #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2105.01717

openalex publication_date 2021/05/04 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28

Abstract

We revisit the fundamental notion of continuity in representation theory,\nwith special attention to the study of quantum physics. After studying the main\ntheorem in the context of representation theory, we draw attention to the\nsignificant aspect of continuity in the analytic foundations of Wigner work. We\nconclude the paper by reviewing the connection between continuity, the\npossibility of defining certain local groups, and their relation to projective\nrepresentations.\n

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