From E & M to QED

This chapter revisits core concepts in electricity and magnetism (E & M), reformulating them using relativistic notation for high-energy physics. It begins with Maxwell's equations, converting them from integral to differential form to identify wave solutions for electric and magnetic fields, thereby demonstrating the electromagnetic nature of light. The introduction of vector and scalar potentials, A and V , is motivated by the divergenceless magnetic field and the need for gauge invariance, ensuring physically observable quantities remain unchanged under transformations. Exercises throughout encourage the application of multivariable calculus theorems to convert integral forms into differential forms and verify gauge invariance. The chapter explores the role of scalar and vector potentials in simplifying electrostatic and electromagnetic calculations, particularly in quantum electrodynamics (QED) and relativistic contexts. It discusses gauge freedom, focusing on the Coulomb and Lorenz gauges and their advantages in electrostatic and relativistic problems. The relativistic formulation of EM introduces the electromagnetic field strength tensor and its transformation properties under Lorentz transformations. The chapter concludes by discussing charge conservation and the transformation of electric and magnetic fields under Lorentz transformations, with exercises reinforcing these concepts.