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- Show that Maxwell equations without sources are invariant for boosts.
- Enunciate the postulates of special relativity, and derive boosts and rotations from them.
- Derive the expression of the Lorentz-Fitzgerald contraction and explain its consequences for the Michelson-Morley experiment.
- Derive the expression of time dilation from Lorentz transformations.
- Explain how 4-momentum must be defined, and derive [math]E=mc^2[/math].
- How do velocity and acceleration vary under boosts?
- Define 4-vectors and give three examples. What does one mean by the terms covariant and contravariant? Define 4-tensors and give two examples.
- Explain what are the properties of Minkowski space-time, and how 4-vectors can be characterised. Give the various canonical forms and the corresponding properties.
- Define the concept of 4-force. What does Newton's second law become in special relativity?
- Show how Maxwell's equations can be rewritten in covariant form. Define the 4-current density.
- Define the field tensor of electromagnetism, and show how the electric and magnetic fields transform under a boost. What are the Lorentz invariants one can build from them?
- What is the electromagnetic field of a moving charge?