| Applied Algebraic Quantum Theory | |||
| Studiengänge Artificial Intelligence Master (PO 2022) Künstliche Intelligenz Technologie Master (PO 2022) Informatik Master Angewandte Mathematik Master | |||
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| Lehrinhalt: Algebraic quantum theory, i.e. the theory of operator algebras and their representations is an important branch of modern functional analysis, connecting non-commutative algebra with topology, measure theory and lattice theory. In the past, many applications in statistical mechanics and quantum field theory have been developed. Yet most recently, algebraic quantum theory appears as a powerful framework for artificial intelligence and cognitive dynamical systems as well. The lecture elucidates the basic concepts of algebraic quantum theory, such as observable algebras, representation theory, and contextual emergence in the light of present and future applications. Keywords: C* dynamical systems, Observables, Ontology, Emergence Literatur: Primas, H. (1981). Chemistry, Quantum Mechanics and Reductionism. Lecture Notes in Chemistry. Springer, Berlin. Haag, R. (1992). Local Quantum Physics: Fields, Particles, Algebras. Texts and Monographs in Physics. Springer, Berlin. Sakai, S. (1971). C*-Algebras and W*-Algebras. Ergebnisse der Mathematik und ihrer Grenzgebiete. Springer, Berlin. beim Graben, P. & Atmanspacher, H. (2006). Complementarity in classical dynamical systems. Foundations of Physics, 36, 291 – 306. beim Graben, P.; Barrett, A. & Atmanspacher, H. (2009). Stability criteria for the contextual emergence of macrostates in neural networks. Network: Computation in Neural Systems, 20, 178 – 196. Carmantini, G. S.; beim Graben, P.; Desroches, M. & Rodrigues, S. (2017). A modular architecture for transparent computation in recurrent neural networks. Neural Networks, 85, 85 – 105. | |||
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