Gauge Invariance of Nonlinear Klein-Gordon

Abstract

We have discussed the gauge invariance of nonlinear Klein-Gordon equation which describes the interaction of electromagnetic initially proposed by Hermann Weyl. The construction of nonlinear Klein-Gordon itself is formulated by two classical conservation laws, Hamilton-Jacobi of relativistic motion and continuity equations. Generally, this equation takes the similar concept to the derivation of the nonlinear master Schrödinger ignoring two fundamental concepts in ordinary quantum mechanics, Einstein and de Broglie’s postulates. In this paper, the proposing for general form of nonlinear Klein-Gordon including the external potential and its gauge invariance have been established. However, we have to ignore the external potential in order to satisfy gauge invariance. In addition, we also prove the derivation of nonlinear Dirac equation for including half-integer spin concept can not hold by similar derivation.

Keywords

• nonlinear Klein-Gordon, gauge invariance.