A non-associative quaternion scalar field theory
  A non-associative Groenewold-Moyal plane is constructed using quaternion-valued function algebras. The symmetrized multi-particle states, the scalar product, the annihilation/creation algebra and d the formulation in terms of a Hopf algebra are also developed. Non-associative quantum algebras in terms of position and momentum operators are given as the simplest examples of a framework whose applications may involve string theory and non-linear quantum field theory 
Sergio Giardino, Paulo Teot\^onio-Sobrinho
math-ph hep-th math.MP