Fractals, Quasicrystals, Chaos, Knots and Algebraic Quantum Mechanics

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At the conclusion of the workshop on "New Theoretical Concepts in Physical Chemistry," a participant shared his impressions, which resonated with the general sentiment, prompting the organizers to use them as a basis for the proceedings. This foreword stems from that context. The workshop covered a broad scope, incorporating contributions from mathematics, physics, crystallography, chemistry, and biology. Problems were approached through both axiomatic methods and empirical phenomenology. This diversity is mirrored in the new concepts introduced, which range from pure theoretical investigations in C*-algebra and quantum probability theory to analyses of complex experimental data, such as nuclear energy levels and phenomena at the intersection of classical and quantum physics. Additionally, some concepts emerged from discoveries of new ordered structures, like icosahedral crystal phases and DNA knots, while others were inspired by applying ideas like fractals and chaos to fields such as spectral theory and chemical reactions. Readers can expect to encounter challenges similar to those faced by participants, as they navigate diverse terminologies, engage with unfamiliar subjects, and grasp sophisticated new concepts.