Chantal Roth, Quaternionic foundations of Quantum Mechanics and spin 1/2 visualization

Prof. Chantal Roth, Quaternionic foundations of Quantum Mechanics and spin 1/2 visualization HyperComplex Seminar 2023, Inaugural lecture Abstract. This talk explores the intriguing link between quaternion quantum mechanics and the model of the elastic continuum proposed by Augustin Cauchy, highlighting the potential of this inter-disciplinary connection to advance our understanding of quantum physics. We elucidate the derivation of non- and relativistic wave equations from the Cauchy theory and Hamilton quaternion algebra, demonstrating how the quaternion representation of the elastic continuum provides a comprehensive picture of quantum mechanics. This innovative interpretation addresses the ontological challenges often associated with quantum theory, o#ering a means to generalize and test the theory. Transitioning from the theoretical to the practical, we delve into a unique visualization of spinors using quaternions. We elucidate how the quaternionic representation enables a comprehension of the