Special Relativity x ElectroMagnetism
DEFINITION
ElectroMagnetism is already Lorentz-Invariant ⇒ No change in Special Relativity!
Just need to update notation to Tensor; check:
| Name | Symbol | Main Change | Formula |
|---|---|---|---|
| Charge | ❌ | ||
| Charge Density | Consider Length Contraction | $$\rho=\gamma(u)\cdot\rho_0$$ | |
| Current Density | Consider Charge Density | $$j^\mu=\rho_0\cdot u^\mu=\begin{bmatrix} \rho\cdot c& \vec{j}\end{bmatrix}$$ | |
| Charge Conservation Law | Consider Current Density | $$\partial_\mu\cdot j^\mu=0$$ | |
| Maxwell Equations | ConsiderCurrent Density & ElectroMagnetic Tensor | ||
| Gauge Transformation | $$\tilde{A}^\mu=A^\mu-\partial_{x^\mu} q$$ | ||
| Lorentz-Gauge Transformation | $$\partial_{x_\mu}A^\mu=0$$ | ||
QUESTIONS
Anki
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