Abstract
In this chapter we define the four-vector of the potentials of the electromagnetic field and relate it to the non-relativistic electric scalar potential and magnetic vector potential. We define the action integral for the motion of a charged particle in the electromagnetic field. Using the variational principle and Lagrange equations we derive the equations of motion of the charged particle, whereby we define the electromagnetic field tensor. By comparison with the Lorentz force on a charged particle in the electromagnetic field, we relate the components of the electromagnetic field tensor to the components of the non-relativistic electric and magnetic field vectors. Thereafter, we study the gauge transformations for the four-potential. Finally, we establish the transformation laws for the electromagnetic field tensor and electromagnetic four-potential and determine the field invariants.
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