Electromagnetism: From First Principles
1) Lagrangian (Action) Formulation
ℒ = −¼ F^{μν} F_{μν} − J^{μ} A_{μ}
2) Why ℒ = −¼ F² is Unique
- 4D Lorentz invariance: all indices must contract to form a scalar.
- U(1) gauge invariance: only F=dA is invariant under A→A+∂Λ.
- At most 2 derivatives: higher-derivative terms are non-renormalizable/irrelevant.
ℒ_free = −¼ F^{μν} F_{μν}
Coupling to sources via −J·A yields the full interacting Lagrangian.
3) Visualize a Plane-Wave (2D)
4) Physical Constants & Energy Density
5) Numeric ℒ Density Visualizer + ℒ Evaluator
a) Static Electric Field (Ex⃗)
b) Static Magnetic Bias (B⃗_off)
c) Compute DC Offsets & AC Amplitude
d) Wave Parameters
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