Nonrelativistic phase-space and octonions (Q750597)

We lack a deeper understanding of the relationship between the macroscopic continuous space of classical physics and the quantum world of elementary particles and their interactions. To make an attempt to disclose the nature of quantum pregeometry centered upon the reinterpretation of quantized spin as one of its basic ingredients, the author seeks a generalization of the classical concept of continuous rotation. First, it is shown that the symmetry group relevant for the nonrelativistic phase space is U(1)\(\times SU(3)\). The SU(3) symmetry group is then considered as the group of automorphisms of the underlying algebra. The sought geometric algebra lies at the origin of phase-space symmetries and is analogous to quaternions. This algebra is shown to be the octonion division algebra of Cayley and Graves. The following part is devoted to automorphisms of octonions and particle symmetries. The last part gives possible developments of the ideas of this paper.