Relativistic Theory of Electrodynamics: the full story
Electromagnetism: Lecture 7 Theoretical physicist Dr Andrew Mitchell presents an undergraduate lecture course on classical Electromagnetism / Electrodynamics at University College Dublin. In this comprehensive lecture, I discuss in detail the theoretical formulation of electromagnetism in terms of Einstein's Special Relativity. I introduce from scratch all the technical and mathematical detail about 4-vectors, Lorentz transformations, and relativistic invariants needed for electrodynamics. I discuss the 4-potential and 4-current, and present the covariant formulation of Maxwell's equations in terms of these objects. I examine the electromagnetic field tensor, and show explicitly how electric and magnetic phenomena become intertwined upon changing inertial reference frame. Finally, I derive the relativistic electrodynamic Lagrangian using powerful general principles of locality, Lorentz invariance, and gauge invariance. From it, the Principle of Least Action yields Maxwell's equations, bringing us full-circle. Full lecture course playlist: • Electromagnetism lecture playlist The textbook "Introduction to Electrodynamics" by Griffiths is recommended reading to accompany this course.
Electromagnetism as a Gauge Theory
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Four-Vectors in special relativity
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Thibault Damour - Einstein's Path to General Relativity
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Special relativity and electrodynamics (covariance, metric tensor, field tensor, potentials)
How Superposition Causes Length Contraction -- And Explains the Principle of Relativity
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