Orthonormal bases, H*-algebras, and nonunital Frobenius algebras
Talk by Dr. Chris Heunen
Speaker invited by: Prof. Dr. Alberto Cattaneo
Date: 26.05.11 Time: 15.15 - 16.15 Room: ETH HG G 43
Categorical quantum mechanics seeks to distill quantum mechanics to minimal assumptions, based on categories with tensor products. We address the question of how to usefully represent observables in this setting. Orthonormal bases in the category of finite-dimensional Hilbert spaces turn out to correspond to Frobenius algebras. We show that for arbitrary dimensions one needs H*-algebras instead, which can be defined in any monoidal category. Finally we compare the notion of H*-algebra to that of nonunital Frobenius algebra in various categories.