Geometric phases for three cases of the electric field with new type Bishop frame in R 1 3

Yoon D. W., Gürbüz N. E.

International Journal of Geometric Methods in Modern Physics, vol.19, 2022 (SCI-Expanded) identifier identifier


© 2022 World Scientific Publishing Company.In this paper, we study geometric phases for an electric field in Minkowski 3-space. In particular, we consider Bishop 2-Type frames of a spacelike and a timelike curve in Minkowski 3-space and investigate three geometric phases for three cases of electric fields with respect to the Bishop 2-Type frames along a spacelike and a timelike curve. Also, we compute spatial and time evolutions of the complex frame connected with electric fields for Bishop 2-Type in terms of modified Hasimoto transformations. As a result, we give a modified Fermi-Walker parallel derivative and a Rytov parallel transportation of electric fields. Finally, we discuss Lorentz force of a magnetic field as a Killing vector field along a spacelike and timelike curve in Minkowski 3-space.