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611: Electromagnetic Theory II CONTENTS • Special relativity; Lorentz covariance of Maxwell equations • Scalar and vector potentials, and gauge invariance • Relativistic motion of charged particles • Action principle for electromagnetism; energy-momentum tensor • Electromagnetic waves; waveguides • Fields due to moving charges • Radiation from accelerating charges • Antennae • Radiation reaction • Magnetic monopoles, duality, Yang-Mills theory Contents 1 Electrodynamics and Special Relativity 4 1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.2 The Lorentz Transformation . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 1.3 4-vectors and 4-tensors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 1.4 Lorentz tensors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 1.5 Proper time and 4-velocity . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 2 Electrodynamics and Maxwell’s Equations 19 2.1 Natural units . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 2.2 Gauge potentials and gauge invariance . . . . . . . . . . . . . . . . . . . . . 19 2.3 21 2.4 Maxwell’s equations in 4-tensor notation . . . . . . . . . . . . . . . . . . . . ~ and B ~ . . . . . . . . . . . . . . . . . . . . . . . Lorentz transformation of E 2.5 The Lorentz force . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 2.6 Action principle for charged particles . . . . . . . . . . . . . . . . . . . . . . 29 2.7 Gauge invariance of the action . . . . . . . . . . . . . . . . .