Cayley-Dickson Procedure, Relativistic Wave Equations and Supersymmetric Oscillators

摘要

The relativistic first-order wave equations for massive particles with spin 0, 1, 1/2 are formulated in terms of a factorization of the Klein-Fock equation by means of the algebra of octonions. An analogous method applied to Hamiltonian of the quantum isotropic oscillator leads to the natural generalization of the model. The class of supersymmetric oscillators with dimensions N ≤ 7 associated with te algebras of the Cayley-Dickson series is introduced.