We consider the factorization of differential operator of Klein–Gordon equation on the base of space-time algebra of sixteen-component sedeons. It is shown that generalized sedeonic wave equations can be used both to describe quantum particles and the force fields responsible for the interaction of particles. In particular, we discuss the first-order and second-order wave equations for sedeonic potentials describing fields with zero and nonzero mass of quantum. We demonstrate the application of sedeonic space-time operators to describe quantum particles and in particular the calculation of energy spectrum of electron in an external magnetic field. The relations between the sedeons and the spinors are discussed.

中文翻译：

---

场论中的Sedeonic方程

我们基于十六分量sedeon的时空代数考虑Klein-Gordon方程的微分算子的因式分解。结果表明，广义的声波方程既可用于描述量子粒子，又可用于引起粒子相互作用的力场。特别是，我们讨论了描述势场为零和非零的场的势能势的一阶和二阶波动方程。我们演示了Sedeonic时空算子在描述量子粒子，特别是在外部磁场中电子能谱的计算中的应用。讨论了sedeon与棘突之间的关系。