Electromagnetic waves along pseudo null curves in Minkowski space

Abstract

Considering the importance of Minkowski space in physics, it is an incomplete approach to deal with EM waves only in Euclidean space. For this reason, this paper deals with EM waves along pseudo null curves in Minkowski space. The main purpose of this study is to examine electromagnetic waves by defining an adapted orthogonal frame along the EM wave which contains both electric and magnetic fields. For this purpose, the extended derivative formulas of pseudo null frame are obtained. Depending on the values of Bishop curvatures, the linear transformations between the pseudo null frame and EM wave vector fields are described in two cases. For all these cases, the relations between these frames are stated, respectively. Moreover, the derivative formulas EM wave vectors are stated by means of geometric phase. Furthermore, the necessary and sufficient conditions provided by the geometric phase are expressed for EM wave vectors to be parallel transportation of the pseudo null frame. Finally, an application is given to investigate the obtained results.