Duplex numbers, diffusion systems, and generalized quantum mechanics
  We show that the relation between the Schr\"odinger equation and diffusion processes has an algebraic nature and can be revealed via the structure of "duplex numbers." This helps one to clarify that quantum mechanics cannot be reduced to diffusion theory. Also, a generalized version of quantum mechanics where $\C$ is replaced by a normed algebra with a unit is proposed. 
Jerzy Kocik
math-ph math.MP quant-ph