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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 . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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2 Electrodynamics and Maxwell’s Equations
19
2.1
Natural units . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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2.2
Gauge potentials and gauge invariance . . . . . . . . . . . . . . . . . . . . .
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2.3
21
2.4
Maxwell’s equations in 4-tensor notation . . . . . . . . . . . . . . . . . . . . ~ and B ~ . . . . . . . . . . . . . . . . . . . . . . . Lorentz transformation of E
2.5
The Lorentz force . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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2.6
Action principle for charged particles . . . . . . . . . . . . . . . . . . . . . .
29
2.7
Gauge invariance of the action . . . . . . . . . . . . . . . . .