Sergio Giardino
Instituto de Matemática e Estatística
Departamento de Matemática Pura e Aplicada (email)
Departamento de Matemática Pura e Aplicada (email)
A nonassociative Groenewold–Moyal (GM) plane is constructed using quaternion-valued function algebras. The symmetrized multiparticle states, the scalar product, the annihilation/creation algebra and the formulation in terms of a Hopf algebra are also developed. Nonassociative 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 nonlinear quantum field theory.