Bücher von Jonathan Steinberg

Generalized probabilistic theories (GPTs) allow us to write quantum theory in a purely operational language and enable us to formulate other, vastly different theories. As it turns out, there is no canonical way to integrate the notion of subsystems within the framework of convex operational theories. Sections can be seen as generalization of subsystems and describe situations where not all possible observables can be implemented. Jonathan Steinberg discusses the mathematical foundations of GPTs using the language of Archimedean order unit spaces and investigates the algebraic nature of sections. This includes an analysis of the category theoretic structure and the transformation properties of the state space. Since the Hilbert space formulation of quantum mechanics uses tensor products to describe subsystems, he shows how one can interpret the tensor product as a special type of a section. In addition he applies this concept to quantum theory and compares it with the formulation in the algebraic approach. Afterwards he gives a complete characterization of low dimensional sections of arbitrary quantum systems using the theory of matrix pencils.

Switzerland is a special and fascinating place. Its unique institutions, its direct democracy, multi-member executives, absence of strikes, communal autonomy, its universal military service, its wealth, and four national languages make it interesting in itself. But it has wider significance, in representing the 'Europe that did not happen', the Europe that escaped the centralisation of state and economy associated with the modern world. Today, there is a new special feature. Switzerland is an island surrounded by the European Union, and resists membership. Why Switzerland? attempts to answer three related questions: why has such an exception to European norms survived? Why should outsiders notice its peculiarities and what can they learn from them? Finally, can so unusual a society continue to exist when many of the conditions in which it evolved have disappeared?