On gauge transformations of electromagnetic potentials in the quaternion form

In this paper, we generalize the Cauchy–Riemann equations of the theory of functions of a complex variable to quaternion functions of eight variables and indicate that some properties of functions of a complex variable remain valid in this case. We propose an interpretation of the system obtained as the system of electrodynamic Maxwell equations and introduce electromagnetic potentials in the quaternionic form. From these general positions, we also introduce gauge transformations and obtain their specific forms.