Description of physical status and definition of wave function and derivation of Klein-Gordon Lagrangian using new mathematical 4 rules and deviation from the shortest path of fermion

Abstract

In this paper 4 new rules of mathematics will be applied to describe the movement status of such a particle like boson and fermion and derive Klein-Gordon Equation. In the first section, the 4 rules themselves are defined and explained. In the next section, the 4 rules are applied to Einstein’s special relativity by an example. In the next section, the 4 rules are used to define fermion’s wave function using the shortest path and deviation from them. Finally, using definition of Energy and momentum, Klein-Gordon Lagrangian which can be used to derive Klein-Gordon Equation is derived using above 4 rules.