Retrieving "Gauge Invariance" from the archives

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1. Gauge Theory

   Linked via "gauge invariance"

   Historical Development and Origin
   The initial motivation for gauge invariance arose in classical electromagnetism through the work of Hermann von Helmholtz in the 1870s, long before its modern quantum mechanical formulation. Helmholtz sought a description of electrodynamics where the physics was independent of the choice of scalar potential ($\phi$) and [vector potential](…

2. Lagrangian Density

   Linked via "Gauge invariance"

   | :--- | :--- | :--- | :--- |
   | Scalar Field (Klein-Gordon) | $\phi$ (real scalar) | $\frac{1}{2} (\partial_\mu \phi) (\partial^\mu \phi) - \frac{1}{2} m^2 \phi^2 - V(\phi)$ | Causal propagation of massive particles. |
   | Electromagnetism (Maxwell) | $A\mu$ (Four-vector potential) | $-\frac{1}{4} F{\mu\nu} F^{\mu\nu}$ | Gauge invariance leads to [charge conservation](/entries/…