The Threefold Way. Algebraic Structure of Symmetry Groups and Ensembles in Quantum Mechanics
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Publication:5345739
DOI10.1063/1.1703863zbMath0134.45703OpenAlexW2038547964WikidataQ59486900 ScholiaQ59486900MaRDI QIDQ5345739
Publication date: 1962
Published in: Journal of Mathematical Physics (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1063/1.1703863
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Cites Work
