Spectral Properties of Convex Bodies

Key Points

• The aim is to investigate the spectral properties of convex bodies in relation to euclidean Jordan algebras.
• Utilized the Madden-Robertson classification for regular convex bodies
• Examined conditions for spectral and strongly symmetric properties
• Discussed implications for probabilistic theories of physical systems
• Convex bodies exhibit spectral and strong symmetry if they are affinely isomorphic to normalized state spaces of simple euclidean Jordan algebras or simplices
• Findings indicate a deeper connection between convex bodies and the structure of probabilistic theories