Journal of Lie Theory

no. 2
Spectral Properties of Convex Bodies
Journal of Lie Theory, Volume 30 (2020) no. 2, pp. 315-344
We use the Madden-Robertson classification of regular convex bodies to show that convex bodies are spectral and strongly symmetric if and only if they are affinely isomorphic to the normalized state spaces of simple euclidean Jordan algebras, or to simplices. Further, we discuss the relevance of this result for general probabilistic theories of quantum and classical physical systems, and its relation to other characterizations of various classes of euclidean Jordan algebra state spaces.
DOI: 10.5802/jolt.1118
Classification: 52Axx, 81P16, 17Cxx
Keywords: Convex bodies, symmetries, spectral theory, euclidean Jordan algebras, homogeneous self-dual cones, quantum information 
@article{JOLT_2020_30_2_a2,
     author = {H. Barnum and J. Hilgert},
     title = {Spectral {Properties} of {Convex} {Bodies}},
     journal = {Journal of Lie Theory},
     pages = {315--344},
     year = {2020},
     volume = {30},
     number = {2},
     doi = {10.5802/jolt.1118},
     zbl = {1440.52004},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.1118/}
}
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H. Barnum; J. Hilgert. Spectral Properties of Convex Bodies. Journal of Lie Theory, Volume 30 (2020) no. 2, pp. 315-344. doi: 10.5802/jolt.1118

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