Abstract: Based on the assumption that physical systems can be characterized by Lagrangians and time progresses in a fixed direction, a dynamical C*-algebra is presented for nonrelativistic particles at atomic scales. This algebra is based on the notion of operations and relies exclusively on classical concepts. Nevertheless, it is inherently non-commutative. Without presupposing any quantization rules, Heisenberg’s commutation relations for position and momentum measurements are derived from it. Hilbert space representations of the algebra lead to the conventional framework of quantum mechanics, but they provide a new view of its foundations. (Joint work with Klaus Fredenhagen.)

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Abstract: We describe a general notion of completeness in QFT. It asserts that the physical observable algebras produced by local degrees of freedom are the maximal ones compatible with causality. We elaborate on equivalent statements to this completeness principle such as the non-existence of generalized symmetries and the uniqueness of the net of algebras. For non-complete theories, we explain how the existence of generalized symmetries is unavoidable, and further, that they always come in dual pairs with precisely the same “size”. Using this new understanding, we argue against the existence of generalized symmetries in the bulk of holographic theories, and prove a recent conjecture by Harlow and Ooguri concerning a universal formula for the charged density of states in QFT.

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Abstract: The concept of a half-sided modular inclusion, i.e. an inclusion of two von Neumann algebras in a particular relative position, is central in the operator-algebraic approach to conformal chiral quantum field theory. Under favourable circumstances, the whole theory on the light ray can be reconstructed from it, including all local algebras and the representation of the Möbius group. An essential requirement is, however, that the inclusion is not singular, i.e. does not have a trivial relative commutant. In this talk I will explain this general setting and then present a technique for producing singular inclusions by a deformation procedure, considering the algebra of observables localized at infinity.

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