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Dynamic Random Walks on Clifford Algebras
"... Multiplicative random walks with dynamic transitions are defined on Clifford algebras of arbitrary signature. These multiplicative walks are then summed to induce additive walks on the algebra. Properties of both types of walks are considered, and limit theorems are developed. ..."
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Multiplicative random walks with dynamic transitions are defined on Clifford algebras of arbitrary signature. These multiplicative walks are then summed to induce additive walks on the algebra. Properties of both types of walks are considered, and limit theorems are developed.
The Theory of Kairons
, 2008
"... In relativistic quantum mechanics wave functions of particles satisfy field equations that have initial data on a space–like hypersurface. We propose a dual field theory of “wavicles ” that have their initial data on a time–like worldline. Propagation of such fields is superluminal, even though the ..."
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In relativistic quantum mechanics wave functions of particles satisfy field equations that have initial data on a space–like hypersurface. We propose a dual field theory of “wavicles ” that have their initial data on a time–like worldline. Propagation of such fields is superluminal, even though the Hilbert space of the solutions carries a unitary representation of the Poincaré group of mass zero. We call the objects described by these field equations “Kairons”. The paper builds the field equations in a general relativistic framework, allowing for a torsion. Kairon fields are section of a vector bundle over spacetime. The bundle has infinite– dimensional fibres. 1