New Applications of Generalised Curves. Particularly in Physics.
Technical summary rept.,
WISCONSIN UNIV-MADISON MATHEMATICS RESEARCH CENTER
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The traditional assumptions of infinitesimal smoothness, implicitly made in various applied topics, do not agree with what is observed at microscopic and smaller dimensions. Mathematical models closer to what actually occurs, are made possible by the theory of generalised curves, and by the matching up and resonance of the infinitesimal patterns they generate. Phenomena hitherto not fully accounted for, may be partly due to such generalised patterns in stress lines of bridges, streamlines of shock waves, and rays of light. In relativistic quantum physics, generalised curves appear on account of the indefiniteness of the metric, and the infinitesimal zigzagging corresponds to successive emission and absorption of radiation. The Nowosad theory, a preview of which is given here, accounts in this way for the elementary particles in a logical manner, and provides at the same time de Broglies Pilot Wave and the quantum potentials of Bohm and Vigier. Moreover such things as the Pauli exclusion become theorems. The theory makes uses of singular integrals and of reduced quaternion-valued analytic functions. Author
- Numerical Mathematics
- Quantum Theory and Relativity