Abstract. Local currents combine the ideas of space-time locality and symme-try by means of an infinite-dimensional Lie algebra of operators. We review some early ideas about relativistic and nonrelativistic local current algebras, and discuss their relation to quantum kinematics. We then summarize three directions of recent research: a model for quantized vortex filaments (with R. Owczarek and D. H. Sharp); a prescription for nonlinear modification of quan-tum mechanics (with H.-D. Doebner); and local currents for a deformed algebra of quantum mechanics (with S. Sarkar). PACS number: 02.20.Tw
A deterministic framework for quantum mechanics is constructed utilizing the split octonionic algebra Osplit. Heisenberg’s uncertainty principle is derived as an algebraic identity from the trivalent associator on the manifold, restricting microscopic state functions to minimal left ideals. The current formulation ensures that quantum uncertainty remains a purely deterministic topological effect, governed by the intrinsic discrete volume constraints of the underlying division algebra. The present framework maps quantum observables directly into a completely deterministic geometric flow, defining the mass quantum as a stable topological soliton on the non-associative worldsheet.