|XXXIV Workshop on Geometric Methods in Physics||28.06-4.07.2015|
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Operator-algebraic quantum foundations revisited
One of the returning main themes in G.G.Emch's work was the programme of using operator algebras as a foundational framework for quantum theory. I will start from reviewing the reasons why this programme has not been completely successful. Next I will discuss some insights and results obtained in other approaches to quantum foundations. Finally, I will show how one can use these insights to revitalise the operator algebraic approach to quantum foundations. The main conceptual and structural changes that I will focus on are, respectively, a shift from ontic to epistemic interpretation of quantum states, and a shift from analysis of intrinsic structures of operator algebras to the geometric structures on the state spaces of these algebras.